On a Verdier quotient of a derived category of a local ring Reviewed

Mifune, Y; Takahashi, R

JOURNAL OF THE MATHEMATICAL SOCIETY OF JAPAN   Vol. 77 ( 2 ) page： 563 - 579   2025.4

Proxy small thick subcategories of derived categories Reviewed

Takahashi, R

JOURNAL OF ALGEBRA   Vol. 662   page： 465 - 481   2025.1

Cofiniteness of local cohomology modules and subcategories of modules Reviewed

Takahashi, R; Wakasugi, N

COLLECTANEA MATHEMATICA   Vol. 76 ( 1 ) page： 1 - 10   2025.1

On a generalization of Ulrich modules and its applications Reviewed

Ela Celikbas; Olgur Celikbas; Justin Lyle; Ryo Takahashi; Yongwei Yao

Tohoku Mathematical Journal     2025

Vanishing of DHKK complexities for singularity categories and generation of syzygy modules Reviewed

Tokuji Araya; Kei-ichiro Iima; Ryo Takahashi

Kyoto Journal of Mathematics     2025

Rings with q-torsionfree canonical modules Reviewed

Naoki Endo; Laura Ghezzi; Shiro Goto; Jooyoun Hong; Shin-ichiro Iai; Toshinori Kobayashi; Naoyuki Matsuoka; Ryo Takahashi

Commutative Algebra: The Mathematical Legacy of Wolmer V. Vasconcelos, edited by Joseph Brennan and Aron Simis, De Gruyter     page： 405 - 426   2025

Ring homomorphisms and local rings with quasi-decomposable maximal ideal Reviewed

Nasseh, S; Sather-Wagstaff, K; Takahashi, R

COMMUNICATIONS IN ALGEBRA   Vol. 52 ( 10 ) page： 4295 - 4313   2024.10

ANNIHILATORS AND DECOMPOSITIONS OF SINGULARITY CATEGORIES Reviewed Open Access

Esentepe, Ö; Takahashi, R

PROCEEDINGS OF THE EDINBURGH MATHEMATICAL SOCIETY   Vol. 67 ( 3 ) page： 699 - 713   2024.8

Auslander-Reiten conjecture and finite injective dimension of Hom Reviewed

Ghosh, D; Takahashi, R

KYOTO JOURNAL OF MATHEMATICS   Vol. 64 ( 1 ) page： 229 - 243   2024.2

When Is a Subcategory Serre or Torsion-Free? Reviewed

Iima, K; Matsui, H; Shimada, K; Takahashi, R

PUBLICATIONS OF THE RESEARCH INSTITUTE FOR MATHEMATICAL SCIENCES   Vol. 60 ( 4 ) page： 831 - 857   2024

Solid generators in module categories and applications Reviewed

Takahashi, R

RENDICONTI DEL SEMINARIO MATEMATICO DELLA UNIVERSITA DI PADOVA   Vol. 152   page： 229 - 243   2024

Remarks on complexities and entropies for singularity categories Reviewed Open Access

Takahashi, R

COMPTES RENDUS MATHEMATIQUE   Vol. 361 ( 1 ) page： 1611 - 1623   2023.11

On the categorical entropy of the Frobenius pushforward functor Reviewed Open Access

Matsui, H; Takahashi, R

BULLETIN OF THE LONDON MATHEMATICAL SOCIETY   Vol. 55 ( 3 ) page： 1358 - 1372   2023.6

Dominant Local Rings and Subcategory Classification Reviewed

Takahashi, R

INTERNATIONAL MATHEMATICS RESEARCH NOTICES   Vol. 2023 ( 9 ) page： 7259 - 7318   2023.5

Faltings' annihilator theorem and <i>t</i>-structures of derived categories Reviewed Open Access

Takahashi, R

MATHEMATISCHE ZEITSCHRIFT   Vol. 304 ( 1 ) page： 1 - 13   2023.5

On the subcategories of <i>n</i>-torsionfree modules and related modules Reviewed

Dey, S; Takahashi, R

COLLECTANEA MATHEMATICA   Vol. 74 ( 1 ) page： 113 - 132   2023.1

Maximal Cohen-Macaulay tensor products and vanishing of Ext modules Reviewed Open Access

Kimura, K; Otake, Y; Takahashi, R

BULLETIN OF THE LONDON MATHEMATICAL SOCIETY   Vol. 54 ( 6 ) page： 2456 - 2468   2022.12

Spanier-Whitehead Categories of Resolving Subcategories and Comparison with Singularity Categories Reviewed

Bahlekeh, A; Salarian, S; Takahashi, R; Toosi, Z

ALGEBRAS AND REPRESENTATION THEORY   Vol. 25 ( 3 ) page： 595 - 613   2022.6

Comparisons Between Annihilators of Tor and Ext Reviewed

Dey, S; Takahashi, R

ACTA MATHEMATICA VIETNAMICA   Vol. 47 ( 1 ) page： 123 - 139   2022.3

Filtrations in Module Categories, Derived Categories, and Prime Spectra Reviewed Open Access

Matsui, H; Takahashi, R

INTERNATIONAL MATHEMATICS RESEARCH NOTICES   Vol. 2022 ( 5 ) page： 3457 - 3492   2022.2

ON REDUCING HOMOLOGICAL DIMENSIONS OVER NOETHERIAN RINGS Reviewed Open Access

Araya, T; Takahashi, R

PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY   Vol. 150 ( 2 ) page： 469 - 480   2022.2

Intersections of resolving subcategories and intersections of thick subcategories Reviewed

Takahashi, R

EUROPEAN JOURNAL OF MATHEMATICS   Vol. 7 ( 4 ) page： 1767 - 1790   2021.12

Grothendieck groups, convex cones and maximal Cohen-Macaulay points Reviewed

Takahashi, R

MATHEMATISCHE ZEITSCHRIFT   Vol. 299 ( 1-2 ) page： 53 - 82   2021.10

Trace ideals of canonical modules, annihilators of Ext modules, and classes of rings close to being Gorenstein Reviewed

Dao, HL; Kobayashi, T; Takahashi, R

JOURNAL OF PURE AND APPLIED ALGEBRA   Vol. 225 ( 9 ) page： 1 - 18   2021.9

Classification of dominant resolving subcategories by moderate functions Reviewed

Takahashi, R

ILLINOIS JOURNAL OF MATHEMATICS   Vol. 65 ( 3 ) page： 597 - 618   2021.9

Some criteria for detecting large homomorphisms of local rings Reviewed Open Access

Gheibi, M; Takahashi, R

COMMUNICATIONS IN ALGEBRA   Vol. 49 ( 8 ) page： 3490 - 3500   2021.7

QUASI-PROJECTIVE DIMENSION Reviewed Open Access

Gheibi, M; Jorgensen, DA; Takahashi, R

PACIFIC JOURNAL OF MATHEMATICS   Vol. 312 ( 1 ) page： 113 - 147   2021.5

Homogeneous prime elements in normal two-dimensional graded rings Reviewed Open Access

Singh, AK; Takahashi, R; Watanabe, K

JOURNAL OF ALGEBRA   Vol. 571   page： 339 - 349   2021.4

The Jacobian ideal of a commutative ring and annihilators of cohomology Reviewed Open Access

Iyengar, SB; Takahashi, R

JOURNAL OF ALGEBRA   Vol. 571   page： 280 - 296   2021.4

COHOMOLOGICAL DIMENSIONS OF SPECIALIZATION-CLOSED SUBSETS AND SUBCATEGORIES OF MODULES Reviewed Open Access

Matsui, H; Nam, TT; Takahashi, R; Tri, NM; Yen, DN

PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY   Vol. 149 ( 2 ) page： 481 - 496   2021.2

POWERS OF THE MAXIMAL IDEAL AND VANISHING OF (CO)HOMOLOGY Reviewed Open Access

Celikbas, O; Takahashi, R

GLASGOW MATHEMATICAL JOURNAL   Vol. 63 ( 1 ) page： 1 - 5   2021.1

Generation in module categories and derived categories of commutative rings Reviewed

Ryo Takahashi

Commutative algebra, Expository Papers Dedicated to David Eisenbud on the Occasion of his 75th Birthday, Springer, Cham     page： 723 - 751   2021

Resolving subcategories whose finitely presented module categories are abelian Reviewed Open Access

Takahashi, R

COMPTES RENDUS MATHEMATIQUE   Vol. 359 ( 5 ) page： 577 - 592   2021

Resolving Subcategories Closed Under Certain Operations and a Conjecture of Dao and Takahashi Reviewed

Sadeghi, A; Takahashi, R

MICHIGAN MATHEMATICAL JOURNAL   Vol. 70 ( 2 ) page： 341 - 367   2021

FLAT RING EPIMORPHISMS AND UNIVERSAL LOCALIZATIONS OF COMMUTATIVE RINGS Reviewed Open Access

Hügel, LA; Marks, F; Stovícek, J; Takahashi, R; Vitória, J

QUARTERLY JOURNAL OF MATHEMATICS   Vol. 71 ( 4 ) page： 1489 - 1520   2020.12

Construction of spectra of triangulated categories and applications to commutative rings Reviewed Open Access

Matsui, H; Takahashi, R

JOURNAL OF THE MATHEMATICAL SOCIETY OF JAPAN   Vol. 72 ( 4 ) page： 1283 - 1307   2020.10

Maximal Cohen-Macaulay modules that are not locally free on the punctured spectrum Reviewed Open Access

Kobayashi, T; Lyle, J; Takahashi, R

JOURNAL OF PURE AND APPLIED ALGEBRA   Vol. 224 ( 7 )   2020.7

A TOPOLOGY ON THE SET OF ISOMORPHISM CLASSES OF MAXIMAL COHEN-MACAULAY MODULES Reviewed Open Access

Hiramatsu, N; Takahashi, R

PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY   Vol. 148 ( 6 ) page： 2359 - 2369   2020.6

On the radius of the category of extensions of matrix factorizations Reviewed Open Access

Shimada, K; Takahashi, R

JOURNAL OF ALGEBRA   Vol. 546   page： 566 - 579   2020.3

Local rings with quasi-decomposable maximal ideal Reviewed Open Access

Nasseh, S; Takahashi, R

MATHEMATICAL PROCEEDINGS OF THE CAMBRIDGE PHILOSOPHICAL SOCIETY   Vol. 168 ( 2 ) page： 305 - 322   2020.3

GORENSTEIN MODIFICATIONS AND Q-GORENSTEIN RINGS Reviewed Open Access

Dao, H; Iyama, O; Takahashi, R; Wemyss, M

JOURNAL OF ALGEBRAIC GEOMETRY   Vol. 29 ( 4 ) page： 729 - 751   2020

Burch ideals and Burch rings Reviewed Open Access

Dao, HL; Kobayashi, T; Takahashi, R

ALGEBRA & NUMBER THEORY   Vol. 14 ( 8 ) page： 2121 - 2150   2020

LITTLE DIMENSION AND THE IMPROVED NEW INTERSECTION THEOREM Reviewed Open Access

Nakamura, T; Takahashi, R; Yassemi, S

MATHEMATICA SCANDINAVICA   Vol. 126 ( 2 ) page： 209 - 220   2020

Generation in singularity categories of hypersurfaces of countable representation type Reviewed

Araya, T; Iima, K; Ono, M; Takahashi, R

ARCHIV DER MATHEMATIK   Vol. 113 ( 6 ) page： 603 - 615   2019.12

Rings whose ideals are isomorphic to trace ideals Reviewed Open Access

Kobayashi, T; Takahashi, R

MATHEMATISCHE NACHRICHTEN   Vol. 292 ( 10 ) page： 2252 - 2261   2019.10

ON THE IDEAL CASE OF A CONJECTURE OF HUNEKE AND WIEGAND Reviewed Open Access

Celikbas, O; Goto, S; Takahashi, R; Taniguchi, N

PROCEEDINGS OF THE EDINBURGH MATHEMATICAL SOCIETY   Vol. 62 ( 3 ) page： 847 - 859   2019.8

ON THE SECOND RIGIDITY THEOREM OF HUNEKE AND WIEGAND Reviewed Open Access

Celikbas, O; Takahashi, R

PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY   Vol. 147 ( 7 ) page： 2733 - 2739   2019.7

On the transitivity of degeneration of modules Reviewed

Takahashi, R

MANUSCRIPTA MATHEMATICA   Vol. 159 ( 3-4 ) page： 431 - 444   2019.7

Ulrich modules over Cohen-Macaulay local rings with minimal multiplicity Reviewed Open Access

Kobayashi, T; Takahashi, R

QUARTERLY JOURNAL OF MATHEMATICS   Vol. 70 ( 2 ) page： 487 - 507   2019.6

Degenerations over (<i>A</i>_∞)-singularities and construction of degenerations over commutative rings Reviewed Open Access

Hiramatsu, N; Takahashi, R; Yoshino, Y

JOURNAL OF ALGEBRA   Vol. 525   page： 374 - 389   2019.5

Remarks on dimensions of triangulated categories Reviewed Open Access

Aihara, T; Takahashi, R

JOURNAL OF ALGEBRA   Vol. 521   page： 235 - 246   2019.3

Applications and homological properties of local rings with decomposable maximal ideals Reviewed Open Access

Nasseh, S; Sather-Wagstaff, S; Takahashi, R; VandeBogert, K

JOURNAL OF PURE AND APPLIED ALGEBRA   Vol. 223 ( 3 ) page： 1272 - 1287   2019.3

Openness of the Regular Locus and Generators for Module Categories Reviewed

Iyengar, SB; Takahashi, R

ACTA MATHEMATICA VIETNAMICA   Vol. 44 ( 1 ) page： 207 - 212   2019.3

Totally reflexive modules and Poincare series Reviewed Open Access

Gheibi, M; Takahashi, R

JOURNAL OF ALGEBRA   Vol. 520   page： 440 - 459   2019.2

Noncommutative resolutions using syzygies Reviewed Open Access

Dao, H; Iyama, O; Iyengar, SB; Takahashi, R; Wemyss, M; Yoshino, Y

BULLETIN OF THE LONDON MATHEMATICAL SOCIETY   Vol. 51 ( 1 ) page： 43 - 48   2019.2

ASSOCIATED PRIMES AND SYZYGIES OF LINKED MODULES Reviewed Open Access

Celikbas, O; Dibaei, MT; Gheibi, M; Sadeghi, A; Takahashi, R

JOURNAL OF COMMUTATIVE ALGEBRA   Vol. 11 ( 3 ) page： 301 - 323   2019

Two generalizations of Auslander-Reiten duality and applications Reviewed

Arash Sadeghi, Ryo Takahashi

  Vol. 63   page： 335 - 351   2019

ON THE VANISHING OF SELF EXTENSIONS OVER COHEN-MACAULAY LOCAL RINGS Reviewed Open Access

Araya, T; Celikbas, O; Sadeghi, A; Takahashi, R

PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY   Vol. 146 ( 11 ) page： 4563 - 4570   2018.11

Structure of Irreducible Homomorphisms to/from Free Modules Reviewed

Nasseh, S; Takahashi, R

ALGEBRAS AND REPRESENTATION THEORY   Vol. 21 ( 2 ) page： 471 - 485   2018.4

On the ideal case of a conjecture of Auslander and Reiten Reviewed Open Access

Celikbas, O; Iima, K; Sadeghi, A; Takahashi, R

BULLETIN DES SCIENCES MATHEMATIQUES   Vol. 142   page： 94 - 107   2018.2

Thick tensor ideals of right bounded derived categories of commutative rings Reviewed

Takahashi, R

REPRESENTATIONS OF ALGEBRAS   Vol. 705   page： 225 - 250   2018

THICK SUBCATEGORIES OVER ISOLATED SINGULARITIES Reviewed Open Access

Takahashi, R

PACIFIC JOURNAL OF MATHEMATICS   Vol. 291 ( 1 ) page： 183 - 211   2017.11

ON THE AUSLANDER-REITEN CONJECTURE FOR COHEN MACAULAY LOCAL RINGS Reviewed Open Access

Goto, S; Takahashi, R

PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY   Vol. 145 ( 8 ) page： 3289 - 3296   2017.8

When are -syzygy modules -torsionfree? Reviewed Open Access

Matsui, H; Takahashi, R; Tsuchiya, Y

ARCHIV DER MATHEMATIK   Vol. 108 ( 4 ) page： 351 - 355   2017.4

Singularity categories and singular equivalences for resolving subcategories Reviewed Open Access

Matsui, H; Takahashi, R

MATHEMATISCHE ZEITSCHRIFT   Vol. 285 ( 1-2 ) page： 251 - 286   2017.2

Thick tensor ideals of right bounded derived categories Reviewed Open Access

Matsui, H; Takahashi, R

ALGEBRA & NUMBER THEORY   Vol. 11 ( 7 ) page： 1677 - 1738   2017

Ulrich ideals and almost Gorenstein rings Reviewed Open Access

Shiro Goto, Ryo Takahashi, Naoki Taniguchi

  Vol. 144   page： 2811-2823   2016

Annihilation of cohomology, generation of modules and finiteness of derived dimension Reviewed Open Access

Abdolnaser Bahlekeh, Ehsan Hakimian, Shokrollah Salarian, Ryo Takahashi

  Vol. 67   page： 387-404   2016

Ulrich ideals and modules over two-dimensional rational singularities Reviewed Open Access

Shiro Goto, Kazuho Ozeki, Ryo Takahashi, Kei-ichi Watanabe, Ken-ichi Yoshida

  Vol. 221   page： 69-110   2016

Extension closedness of syzygies and local Gorensteinness of commutative rings Reviewed Open Access

Shiro Goto, Ryo Takahashi

  Vol. 19   page： 511-521   2016

Perfect linkage of Cohen-Macaulay modules over Cohen-Macaulay rings Reviewed Open Access

Kei-ichiro Iima, Ryo Takahashi

  Vol. 458   page： 134-155   2016

Annihilation of cohomology and strong generation of module categories Reviewed

Srikanth B. Iyengar, Ryo Takahashi

International Mathematics Research Notices. IMRN   Vol. 2016   page： 499-535   2016

Huneke-Wiegand conjecture and change of rings Reviewed

Shiro Goto, Ryo Takahashi, Naoki Taniguchi, Hoang Le Truong

J. Algebra   Vol. 422   page： 33-52   2015

The dimension of a subcategory of modules Reviewed

Hailong Dao, Ryo Takahashi

Forum of Mathematics. Sigma   Vol. 3 ( 19 ) page： 1 - 31   2015

Generators and dimensions of derived categories of modules Reviewed

Takuma Aihara, Ryo Takahashi

Communications in Algebra   Vol. 43   page： 5003-5029   2015

Endofunctors of singularity categories characterizing Gorenstein rings Reviewed Open Access

Takuma Aihara, Ryo Takahashi

Proceedings of the American Mathematical Society   Vol. 143   page： 3777-3779   2015

Non-commutative resolutions and Grothendieck groups Reviewed Open Access

Hailong Dao, Osamu Iyama, Ryo Takahashi, Charles Vial

J. Noncommut. Geom.   Vol. 9   page： 21-34   2015

Maximal Cohen-Macaulay approximations and Serre's condition Reviewed

Hiroki Matsui, Ryo Takahashi

Acta Math. Vietnam.   Vol. 40   page： 197-203   2015

Building modules from the singular locus Reviewed

Jesse Burke, Lars Winther Christensen, Ryo Takahashi

Math. Scand.   Vol. 116   page： 23-33   2015

Upper bounds for dimensions of singularity categories Reviewed Open Access

Hailong Dao, Ryo Takahashi

C. R. Math. Acad. Sci. Paris   Vol. 353   page： 297-301   2015

Almost Gorenstein rings -- towards a theory of higher dimension -- Reviewed

Shiro Goto, Ryo Takahashi, Naoki Taniguchi

J. Pure Appl. Algebra   Vol. 219   page： 2666-2712   2015

Bounds on depth of tensor products of modules Reviewed Open Access

Olgur Celikbas, Arashi Sadeghi, Ryo Takahashi

J. Pure Appl. Algebra   Vol. 219   page： 1670-1684   2015

Classification of resolving subcategories and grade consistent functions Reviewed

Hailong Dao, Ryo Takahashi

Int. Math. Res. Not. IMRN   Vol. 2015   page： 119-149   2015

Ulrich ideals and modules Reviewed

Shiro Goto, Kazuho Ozeki, Ryo Takahashi, Kei-ichi Watanabe, Ken-ichi Yoshida

Math. Proc. Cambridge Philos. Soc.   Vol. 156 ( 1 ) page： 137-166   2014

Annihilation of cohomology and decompositions of derived categories Reviewed Open Access

Srikanth B. Iyengar, Ryo Takahashi

Homology, Homotopy Appl.   Vol. 16 ( 2 ) page： 231-237   2014

Modules that detect finite homological dimensions Reviewed Open Access

Olgur Celikbas, Hailong Dao, Ryo Takahashi

Kyoto J. Math.   Vol. 54 ( 2 ) page： 295-310   2014

Brauer-Thrall for totally reflexive modules over local rings of higher dimension Reviewed Open Access

Olgur Celikbas, Mohsen Gheibi, Ryo Takahashi

Algebr. Represent. Theory   Vol. 17 ( 3 ) page： 997-1008   2014

Reconstruction from Koszul homology and applications to module and derived categories Reviewed Open Access

Ryo Takahashi

Pacific J. Math.   Vol. 268 ( 1 ) page： 231-248   2014

The radius of a subcategory of modules Reviewed Open Access

Hailong Dao, Ryo Takahashi

Algebra Number Theory   Vol. 8 ( 1 ) page： 141-172   2014

Dimensions of triangulated categories with respect to subcategories Reviewed

Takuma Aihara, Tokuji Araya, Osamu Iyama, Ryo Takahashi, Michio Yoshiwaki

J. Algebra   Vol. 399   page： 205-219   2014

Classifying resolving subcategories over a Cohen-Macaulay local ring Reviewed

Ryo Takahashi

Math. Z.   Vol. 273 ( 1 ) page： 569-587   2013

Thick subcategories over Gorenstein local rings that are locally hypersurfaces on the punctured spectra Reviewed Open Access

Ryo Takahashi

J. Math. Soc. Japan   Vol. 65 ( 2 ) page： 357-374   2013

Tilting and cluster tilting for quotient singularities Reviewed

Osamu Iyama, Ryo Takahashi

Math. Ann.   Vol. 356 ( 3 ) page： 1065-1105   2013

Auslander-Reiten conjecture and Auslander-Reiten duality Reviewed Open Access

O. Celikbas, R. Takahashi

J. Algebra   Vol. 382   page： 100-114   2013

On the left perpendicular category of the modules of finite projective dimension Reviewed

Tokuji Araya, Kei-ichiro Iima, Ryo Takahashi

Comm. Algebra   Vol. 40 ( 8 ) page： 2693-2699   2012

On the structure of Cohen-Macaulay modules over hypersurfaces of countable Cohen-Macaulay representation type Reviewed

T. Araya, K.-i. Iima, R. Takahashi

J. Algebra   Vol. 361   page： 213-224   2012

Contravariantly finite resolving subcategories over commutative rings Reviewed Open Access

R. Takahashi

Amer. J. Math.   Vol. 133 ( 2 ) page： 417-436   2011

When is there a nontrivial extension-closed subcategory? Reviewed

R. Takahashi

J. Algebra   Vol. 331 ( 1 ) page： 388-399   2011

Homological aspects of semidualizing modules Reviewed

R. Takahashi, D. White

Math. Scand.   Vol. 106 ( 1 ) page： 5-22   2010

On the existence of embeddings into modules of finite homological dimensions Reviewed Open Access

R. Takahashi, S. Yassemi, Y. Yoshino

Proc. Amer. Math. Soc.   Vol. 138 ( 7 ) page： 2265-2268   2010

Classifying thick subcategories of the stable category of Cohen-Macaulay modules Reviewed

R. Takahashi

Adv. Math.   Vol. 225 ( 4 ) page： 2076-2116   2010

On localizing subcategories of derived categories Reviewed Open Access

R. Takahashi

J. Math. Kyoto Univ.   Vol. 49 ( 4 ) page： 771-783   2009

Local cohomology based on a nonclosed support defined by a pair of ideals Reviewed

R. Takahashi, Y. Yoshino, T. Yoshizawa

J. Pure Appl. Algebra   Vol. 213 ( 4 ) page： 582-600   2009

Modules in resolving subcategories which are free on the punctured spectrum Reviewed Open Access

R. Takahashi

Pacific J. Math.   Vol. 241 ( 2 ) page： 347-367   2009

A generalization of a theorem of Foxby Reviewed

T. Araya, R. Takahashi

Arch. Math. (Basel)   Vol. 93 ( 2 ) page： 123-127   2009

Classifying subcategories of modules over a commutative noetherian ring Reviewed Open Access

R. Takahashi

J. Lond. Math. Soc. (2)   Vol. 78 ( 3 ) page： 767-782   2008

Quasi-socle ideals in a Gorenstein local ring Reviewed

S. Goto, R. Takahashi, N. Matsuoka

J. Pure Appl. Algebra   Vol. 212 ( 5 ) page： 969-980   2008

Direct summands of syzygy modules of the residue class field Reviewed

R. Takahashi

Nagoya Math. J.   Vol. 189   page： 1-25   2008

D-modules over rings with finite F-representation type Reviewed Open Access

S. Takagi, R. Takahashi

Math. Res. Lett.   Vol. 15 ( 3 ) page： 563-581   2008

Finite Gorenstein representation type implies simple singularity Reviewed

L. W. Christensen, G. Piepmeyer, J. Striuli, R. Takahashi

Adv. Math.   Vol. 218 ( 4 ) page： 1012-1026   2008

On vanishing of certain Ext modules Reviewed Open Access

S. Goto, F. Hayasaka, R. Takahashi

J. Math. Soc. Japan   Vol. 60 ( 4 ) page： 1045-1064   2008

On G-regular local rings Reviewed

R. Takahashi

Comm. Algebra   Vol. 36 ( 12 ) page： 4472-4491   2008

An uncountably infinite number of indecomposable totally reflexive modules Reviewed Open Access

R. Takahashi

Nagoya Math. J.   Vol. 187   page： 35-48   2007

A new approximation theory which unifies spherical and Cohen-Macaulay approximations Reviewed

R. Takahashi

J. Pure Appl. Algebra   Vol. 208 ( 2 ) page： 617-634   2007

On the number of indecomposable totally reflexive modules Reviewed

R. Takahashi

Bull. London Math. Soc.   Vol. 39 ( 3 ) page： 487-492   2007

Totally reflexive modules constructed from smooth projective curves of genus g >= 2 Reviewed

R. Takahashi, K.-i. Watanabe

Arch. Math. (Basel)   Vol. 89 ( 1 ) page： 60-67   2007

A characterization of modules locally of finite injective dimension Reviewed Open Access

R. Takahashi

Proc. Amer. Math. Soc.   Vol. 135 ( 11 ) page： 3461-3464   2007

Openness of FID-loci Reviewed Open Access

R. Takahashi

Glasg. Math. J.   Vol. 48 ( 3 ) page： 431-435   2006

Syzygy modules with semidualizing or G-projective summands Reviewed

R. Takahashi

J. Algebra   Vol. 295 ( 1 ) page： 179-194   2006

A note on a theorem of F. Wang and G. Tang Reviewed

R. Takahashi

Bull. Austral. Math. Soc.   Vol. 73   page： 293-297   2006

Remarks on modules approximated by G-projective modules Reviewed

R. Takahashi

J. Algebra   Vol. 301 ( 2 ) page： 748-780   2006

The existence of finitely generated modules of finite Gorenstein injective dimension Reviewed Open Access

R. Takahashi

Proc. Amer. Math. Soc.   Vol. 134 ( 11 ) page： 3115-3121   2006

On the category of modules of Gorenstein dimension zero Reviewed

R. Takahashi

Math. Z.   Vol. 251 ( 2 ) page： 249-256   2005

Homological invariants associated to semi-dualizing bimodules Reviewed Open Access

T. Araya, R. Takahashi, Y. Yoshino

J. Math. Kyoto Univ.   Vol. 45 ( 2 ) page： 287-306   2005

Modules of G-dimension zero over local rings of depth two Reviewed Open Access

R. Takahashi

Illinois J. Math.   Vol. 48 ( 3 ) page： 945-952   2004

Upper complete intersection dimension relative to a local homomorphism Reviewed

R. Takahashi

Tokyo J. Math.   Vol. 27 ( 1 ) page： 209-219   2004

On the category of modules of Gorenstein dimension zero II Reviewed

R. Takahashi

J. Algebra   Vol. 278 ( 1 ) page： 402-410   2004

Characterizing Cohen-Macaulay local rings by Frobenius maps Reviewed Open Access

R. Takahashi, Y. Yoshino

Proc. Amer. Math. Soc.   Vol. 132 ( 11 ) page： 3177-3187   2004

Some characterizations of Gorenstein local rings in terms of G-dimension Reviewed

R. Takahashi

Acta Math. Hungar.   Vol. 104 ( 4 ) page： 315-322   2004

Upper Cohen-Macaulay dimension Reviewed

T. Araya, R. Takahashi, Y. Yoshino

Math. J. Okayama Univ.   Vol. 46   page： 17-30   2004

Nagata criterion for Serre's (Rn) and (Sn)-conditions Reviewed

R. Takahashi

Math. J. Okayama Univ.   Vol. 41   page： 37-43   1999

Foundations of rigid geometry from birational viewpoint

Grant number：15H03607  2015.4 - 2019.3

FUJIWARA KAZUHIRO