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Communications in Algebra Volume 26, 1998 - Issue 11
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Original Articles

Remarks on a depth formula, a grade inequality and a conjecture of Auslander

Tokuji Araya Graduate School of Human and Environmental Studies, Kyoto University, Kyoto, 606-01, Japan
&
Yuji Yoshino Inst. of Math., Faculty of Integrated Human Studies, Kyoto University, Kyoto, 606-01, Japan
Pages 3793-3806 | Received 01 Jul 1997, Published online: 23 Dec 2010

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Victor H. Jorge-Pérez & Cleto B. Miranda-Neto. (2021) Criteria for prescribed bound on projective dimension. Communications in Algebra 49:6, pages 2505-2515.
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Parviz Sahandi, Tirdad Sharif & Siamak Yassemi. (2011) Depth Formula via Complete Intersection Flat Dimension. Communications in Algebra 39:11, pages 4002-4013.
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Siamak Yassemi, Leila Khatami & Tirdad Sharif. (2001) GRADE AND GORENSTEIN DIMENSION. Communications in Algebra 29:11, pages 5085-5094.
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Sangki Choi & Srikanth Iyengar. (2001) ON A DEPTH FORMULA FOR MODULES OVER LOCAL RINGS. Communications in Algebra 29:7, pages 3135-3143.
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David A. Jorgensen. (2001) VANISHING OF (CO)HOMOLOGY OVER COMMUTATIVE RINGS. Communications in Algebra 29:5, pages 1883-1898.
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Samir Bouchiba. (2022) On maximal ideals of the polynomial ring and some conjectures on Ext-index of rings. Journal of Algebra and Its Applications 23:03.
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Olgur Celikbas, Li Liang, Arash Sadeghi & Tirdad Sharif. (2023) A Study of Tate Homology via the Approximation Theory with Applications to the Depth Formula. Acta Mathematica Sinica, English Series 39:3, pages 439-458.
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Maryam Salimi & Elham Tavasoli. (2023) Relative grade and relative Gorenstein dimension with respect to a semidualizing module. Proceedings - Mathematical Sciences 133:1.
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Dipankar Ghosh & Ryo Takahashi. (2023) Auslander–Reiten conjecture and finite injective dimension of Hom. Kyoto Journal of Mathematics -1:-1.
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Samir Bouchiba & Salah Kabbaj. (2022) ON THE FINITENESS OF EXT-INDICES OF RING EXTENSIONS. Rocky Mountain Journal of Mathematics 52:6.
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Saeed Nasseh, Maiko Ono & Yuji Yoshino. (2022) Naïve liftings of DG modules. Mathematische Zeitschrift 301:1, pages 1191-1210.
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Ryo Takahashi. (2021) Intersections of resolving subcategories and intersections of thick subcategories. European Journal of Mathematics 7:4, pages 1767-1790.
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Mohsen Gheibi, David A. Jorgensen & Ryo Takahashi. (2021) Quasi-projective dimension. Pacific Journal of Mathematics 312:1, pages 113-147.
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Olgur Celikbas & Arash Sadeghi. (2020) Maximal Cohen–Macaulay tensor products. Annali di Matematica Pura ed Applicata (1923 -) 200:3, pages 923-944.
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Olgur Celikbas, Hiroki Matsui & Arash Sadeghi. 2021. Commutative Algebra. Commutative Algebra 1 10 .
Olgur Celikbas. (2020) On the vanishing of the theta invariant and a conjecture of Huneke and Wiegand. Pacific Journal of Mathematics 309:1, pages 103-144.
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Justin Lyle & Jonathan Montaño. (2020) Extremal growth of Betti numbers and trivial vanishing of (co)homology. Transactions of the American Mathematical Society 373:11, pages 7937-7958.
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Olgur Celikbas, Arash Sadeghi & Naoki Taniguchi. (2019) On Modules with Reducible Complexity. Algebras and Representation Theory 23:4, pages 1467-1476.
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Tokuji Araya & Olgur Celikbas. (2020) Reducing invariants and total reflexivity. Illinois Journal of Mathematics 64:2.
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Tokuji Araya. (2018) A homological dimension related to AB rings. Beiträge zur Algebra und Geometrie / Contributions to Algebra and Geometry 60:2, pages 225-231.
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Saeed Nasseh & Ryo Takahashi. (2017) Structure of Irreducible Homomorphisms to/from Free Modules. Algebras and Representation Theory 21:2, pages 471-485.
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Olgur Celikbas, Kei-ichiro Iima, Arash Sadeghi & Ryo Takahashi. (2018) On the ideal case of a conjecture of Auslander and Reiten. Bulletin des Sciences Mathématiques 142, pages 94-107.
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Saeed Nasseh & Sean Sather-Wagstaff. (2017) Vanishing of Ext and Tor over fiber products. Proceedings of the American Mathematical Society 145:11, pages 4661-4674.
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Olgur Celikbas, Li Liang & Arash Sadeghi. (2017) Vanishing of relative homology and depth of tensor products. Journal of Algebra 478, pages 382-396.
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Yan Ping Liu, Zhong Kui Liu & Xiao Yan Yang. (2016) Vanishing of Tate homology — An application of stable homology for complexes. Acta Mathematica Sinica, English Series 32:7, pages 831-844.
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Mohammad T. Dibaei & Arash Sadeghi. (2015) Linkage of modules and the Serre conditions. Journal of Pure and Applied Algebra 219:10, pages 4458-4478.
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ARASH SADEGHI. (2014) VANISHING OF COHOMOLOGY OVER COMPLETE INTERSECTION RINGS. Glasgow Mathematical Journal 57:2, pages 445-455.
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Olgur Celikbas, Arash Sadeghi & Ryo Takahashi. (2015) Bounds on depth of tensor products of modules. Journal of Pure and Applied Algebra 219:5, pages 1670-1684.
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Lars Winther Christensen & David A. Jorgensen. (2015) Vanishing of Tate homology and depth formulas over local rings. Journal of Pure and Applied Algebra 219:3, pages 464-481.
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Olgur Celikbas & Roger Wiegand. (2015) Vanishing of Tor, and why we care about it. Journal of Pure and Applied Algebra 219:3, pages 429-448.
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Olgur Celikbas & Hailong Dao. (2014) Necessary conditions for the depth formula over Cohen–Macaulay local rings. Journal of Pure and Applied Algebra 218:3, pages 522-530.
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Yihua Liao & Jianlong Chen. (2013) Approximations and cotorsion pairs related to a tilting pair. Frontiers of Mathematics in China 8:6, pages 1367-1376.
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Saeed Nasseh & Massoud Tousi. (2013) A note on symmetry in the vanishing of Ext. Rocky Mountain Journal of Mathematics 43:1.
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Olgur Celikbas & Hailong Dao. (2010) Asymptotic behavior of Ext functors for modules of finite complete intersection dimension. Mathematische Zeitschrift 269:3-4, pages 1005-1020.
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Olgur Celikbas. (2011) Vanishing of TOR over complete intersections. Journal of Commutative Algebra 3:2.
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Petter Andreas Bergh & David A. Jorgensen. (2011) On the vanishing of homology for modules of finite complete intersection dimension. Journal of Pure and Applied Algebra 215:3, pages 242-252.
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Petter Andreas Bergh & David A. Jorgensen. (2011) The depth formula for modules with reducible complexity. Illinois Journal of Mathematics 55:2.
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David A. Jorgensen. (2009) On tensor products of rings and extension conjectures. Journal of Commutative Algebra 1:4.
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D. A. Jorgensen & W. F. Moore. (2009) Minimal Intersections and vanishing (co)homology. Journal of Commutative Algebra 1:3.
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Saeed Nasseh & Yuji Yoshino. (2009) On Ext-indices of ring extensions. Journal of Pure and Applied Algebra 213:7, pages 1216-1223.
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Tokuji Araya. (2008) The Auslander-Reiten conjecture for Gorenstein rings. Proceedings of the American Mathematical Society 137:6, pages 1941-1944.
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Petter Bergh. (2007) On support varieties for modules over complete intersections. Proceedings of the American Mathematical Society 135:12, pages 3795-3803.
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Petter Andreas Bergh. (2007) Modules with reducible complexity. Journal of Algebra 310:1, pages 132-147.
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A. A. Gerko. (2007) Homological dimensions and semidualizing complexes. Journal of Mathematical Sciences 142:4, pages 2205-2232.
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David A. Jorgensen & Liana M. Şega. (2004) Nonvanishing cohomology and classes of Gorenstein rings. Advances in Mathematics 188:2, pages 470-490.
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Александр Александрович Герко & Aleksander Aleksandrovich Gerko. (2001) О гомологических размерностяхOn homological dimensions. Математический сборник Matematicheskii Sbornik 192:8, pages 79-94.
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