Results 1 to 10 of about 132 (127)
On Degenerations of Cohen–Macaulay Modules
Journal of Algebra, 2002 A theorem of M. Auslander states that the isomorphism class of a finitely generated module \(M\) over a finite dimensional algebra \(A\) over a field is determined by the lengths of \(\Hom_A(M,N)\), where \(N\) runs through the finitely generated \(A\)-modules. A proof that makes no use of Auslander-Reiten sequences was given by \textit{K.
Yuji Yoshino
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On the structure of sequentially generalized Cohen–Macaulay modules
Journal of Algebra, 2007 28 ...
Nguyen Tu Cuong
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Communications in Algebra, 2001 A commutative noetherian ring R is called an almost Cohen–Macaulay ring if depth(P, R) = depth(P R P , R P ) for every P ∈ SpecR. [It was called a D-ring by Han (Acta Math. Sinica 1998, 4, 1047–1052).] Several fundamental properties of almost Cohen–Macaulay rings were estabished by Han.
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A NOTE ON BALANCED BIG COHEN–MACAULAY MODULES [PDF]
Journal of Algebraic Systems, 2021 Let $(R, m, k)$ be a Cohen-Macaulay complete local ring with the canonical module $\omega$. The aim of this note, is to show that, under mild assumptions, the class of balanced big Cohen--Macaulay modules coincides with the one consisting of those ...
Abdol N. Bahlekeh
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TWO PROPERTIES OF COUSIN FUNCTORS [PDF]
Journal of Algebraic Systems, 2023 Let $R$ be a commutative Noetherian ring with non-zero identity and $\mathcal{F}$ a filtration of $\operatorname{Spec}(R)$. We show that the Cousin functor with respect to $\mathcal{F}$, $C_R(\mathcal{F},-):\mathcal{C}_{\mathcal{F}}(R ...
Alireza Vahidi +2 more
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LINKAGE OF IDEALS OVER A MODULE [PDF]
Journal of Algebraic Systems, 2021 Inspired by the works in linkage theory of ideals, we define the concept of linkage of ideals over a module. Several known theorems in linkage theory are improved or recovered.
M. Jahangiri, Kh. Sayyari
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ON THE PROJECTIVE DIMENSION OF ARTINIAN MODULES [PDF]
Journal of Algebraic Systems, 2021 Let $(R, \mathfrak{m})$ be a Noetherian local ring and $M$, $N$ be two finitely generated $R$-modules. In this paper it is shown that $R$ is a Cohen-Macaulay ring if and only if $R$ admits a non-zero Artinian $R$-module $A$ of finite projective dimension;
Y. Irani, K. Bahmanpour, Gh. Ghasemi
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Skew graded $(A_\infty )$ hypersurface singularities
Comptes Rendus. Mathématique, 2023 For a skew version of a graded $(A_\infty )$ hypersurface singularity $A$, we study the stable category of graded maximal Cohen-Macaulay modules over $A$.
Ueyama, Kenta
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On the properties of weak CM rings
上海师范大学学报. 自然科学版, 2022 In this paper, we mainly study the properties of weak CM rings. It is a special class of Noetherian commutative rings, including Cohen-Macaulay rings, excellent rings and generalized Cohen-Macaulay rings, which can be characterized by local cohomology ...
XUE Wensi, ZHOU Caijun
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Acyclic Complexes and Graded Algebras
Mathematics, 2023 We already know that the noncommutative N-graded Noetherian algebras resemble commutative local Noetherian rings in many respects. We also know that commutative rings have the important property that every minimal acyclic complex of finitely generated ...
Chaoyuan Zhou
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