Results 141 to 150 of about 769,852 (175)

Local Cohen–Macaulay DG-Modules

Applied Categorical Structures, 2023
In the classical theory of commutative algebras, the Cohen-Macaulay properties of rings and modules are fundamental and important. It is meaningful to generalize the theory of Cohen-Macaulay rings and modules to the DG context. \textit{L. Shaul} has done some interesting research on this topic in [Trans. Am. Math. Soc. 373, No. 9, 6095--6138 (2020; Zbl
Xiaoyan Yang, Yanjie Li
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Maximal Cohen–Macaulay Modules and Gorenstein Algebras [PDF]

Journal of Algebra, 2001
Let B be a graded Cohen–Macaulay quotient of a Gorenstein ring, R. It is known that sections of the dual of the canonical module, KB, can be used to construct Gorenstein quotients of R.
Chris Peterson
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Cohen–Macaulay properties for balanced big Cohen–Macaulay modules

Mathematical Proceedings of the Cambridge Philosophical Society, 1981
Let A be a (commutative, Noetherian) local ring (with identity) and let a1,…, an be a system of parameters (s.o.p.) for A. A (not necessarily finitely generated) A-module M is said to be a big Cohen–Macaulay.A-module with respect to a1,…, an if a1,…, an is an M-sequence, that is if M ‡ = (a1,…, an) M and, for each i = 1,…, n,One of the main open ...
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A note on almost Cohen–Macaulay modules

Journal of Algebra and Its Applications, 2015
In this paper, we give some necessary and sufficient conditions of a module to be an almost Cohen–Macaulay module by using a characterization of the associated primes set of the first non-vanishing local cohomology module. Also, we give a class of examples of almost Cohen–Macaulay modules.
Chu, Lizhong, Tang, Zhongming, Tang, Hui
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Cohen-Macaulay Modules for Graded Cohen-Macaulay Rings and their Completions

1989
Let ℤ denote the integers and \(R = \coprod\nolimits_{i \in \mathbb{Z}} {{R_i}} \) a ℤ-graded commutative ring with R 0 = k a field, R i = (0) when i {\text{0}}} {{R_i}} \). When R is Cohen-Macaulay, we shall study the relationship between R and \(\hat R\), especially with respect to almost split sequences for Cohen-Macaulay modules.
Maurice Auslander, Idun Reiten
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Results on almost Cohen-Macaulay modules

2015
Summary: Let \((R,\underline{m})\) be a commutative Noetherian local ring, and \(M\) be a non-zero finitely generated \(R\)-module. We show that if \(R\) is almost Cohen-Macaulay and \(M\) is perfect with finite projective dimension, then \(M\) is an almost Cohen-Macaulay module.
Mafi, A., Tabejamaat, S.
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Compactness of the Alexandrov topology of maximal Cohen–Macaulay modules

Communications in Algebra
Let $R$ be a Cohen-Macaulay local ring. In this paper, we first describe the radicals of annihilators of stable categories of maximal Cohen-Macaulay $R$-modules. We then prove that the Alexandrov topology of the stable category of maximal Cohen-Macaulay $
Kaito Kimura
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