Results 1 to 10 of about 95 (86)
GENERALIZED FORMAL LOCAL COHOMOLOGY MODULES [PDF]
Journal of Algebraic Systems, 2023 Let $a$ be an ideal of a local ring $(R, m)$ and $M$ and $N$ two finitely generated $R$-modules. In this paper, we introduce the concept of generalized formal local cohomology modules. We define $i$-th generalized formal local cohomology module of $M$
Shahram Rezaei, Fatemeh Lashkari
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Extension Functors of Generalized Local Cohomology Modules
پژوهشهای ریاضی, 2021 Introduction Throughout this paper, is a commutative Noetherian ring with non-zero identity, is an ideal of , is a finitely generated -module, and is an arbitrary -module which is not necessarily finitely generated.
Alireza Vahidi +2 more
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Some Results on Generalized Local Cohomology Modules [PDF]
Communications in Algebra, 2015 Let $R$ be a commutative Noetherian ring with non-zero identity, $\fa$ an ideal of $R$, $M$ a finite $R$--module and $X$ an arbitrary $R$--module. Here, we show that, in the Serre subcategories of the category of $R$--modules, how the generalized local cohomology modules, the ordinary local cohomology modules and the extension modules behave similarly ...
Moharram Aghapournahr, Alireza Vahidi
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UPPER BOUNDS FOR FINITENESS OF GENERALIZED LOCAL COHOMOLOGY MODULES [PDF]
Journal of Algebraic Systems, 2013 Let $R$ be a commutative Noetherian ring with non-zero identity and $fa$ an ideal of $R$. Let $M$ be a finite $R$--module of finite projective dimension and $N$ an arbitrary finite $R$--module.
Moharram Aghapournahr
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On the cofiniteness of generalized local cohomology modules
Bulletin of the Belgian Mathematical Society - Simon Stevin, 2020 Let \(R\) be a commutative noetherian ring, \(\mathfrak{a}\) an ideal of \(R\), and \(M\) and \(N\) two \(R\)-modules. Herzog defined the \(i\)th generalized local cohomology module of \(M\) and \(N\) with respect to \(\mathfrak{a}\) as follows: \[H^{i}_{\mathfrak{a}}(M,N) = \underset{n\in \mathbb{N}}\varinjlim \operatorname{Ext}^{i}_{R}(M/\mathfrak{a}^
Vahdanipour, Farzaneh +2 more
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Filter Regular Sequences and Generalized Local Cohomology Modules [PDF]
Bulletin of the Malaysian Mathematical Sciences Society, 2014 Let $\frak a$, $\frak b$ be ideals of a commutative Noetherian ring $R$ and let $M$, $N$ be finite $R$-modules. The concept of an $\frak a$-filter grade of $\frak b$ on $M$ is introduced and several characterizations and properties of this notion are given.
Ali Fathi, Hossein Zakeri
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On the cofiniteness of generalized local cohomology modules
Kyoto Journal of Mathematics, 2015 Let $R$ be a commutative Noetherian ring, $I$ an ideal of $R$ and $M$, $N$ two finitely generated $R$-modules. The aim of this paper is to investigate the $I$-cofiniteness of generalized local cohomology modules $\displaystyle H^j_I(M,N)=\dlim\Ext^j_R(M/I^nM,N)$ of $M$ and $N$ with respect to $I$. We first prove that if $I$ is a principal ideal then $H^
Shiro Gotō, Nguyen Tu Cuong
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FALTINGS’ LOCAL-GLOBAL PRINCIPLE FOR THE MINIMAXNESS OF LOCAL COHOMOLOGY MODULES DEFINED BY A SYSTEM OF IDEALS [PDF]
Journal of Algebraic Systems, 2023 Let R be a commutative Noetherian ring with nonzero identity. Let φ be a system of ideals of R and let M, N two finitely generated R-modules. We prove that there are local- global principles for the finiteness and minimaxness of generalized local ...
F. Dehghani-Zadeh, A.R. Hajikarimi
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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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On Vanishing of Generalized Local Cohomology Modules [PDF]
Algebra Colloquium, 2005 Let [Formula: see text] denote an ideal of a d-dimensional Gorenstein local ring R, and M and N two finitely generated R-modules with pd M < ∞. It is shown that [Formula: see text] if and only if [Formula: see text] for all [Formula: see text].
Divaani-Aazar, K. +2 more
openaire +3 more sources