Affiliation:
1. Department of Mathematics, Faculty of Sciences, University of Mohaghegh Ardabili, 56199-11367, Ardabil, Iran
Abstract
Let [Formula: see text] be a commutative Noetherian complete local ring and [Formula: see text] be a proper ideal of [Formula: see text]. Suppose that [Formula: see text] is a nonzero [Formula: see text]-cofinite [Formula: see text]-module of Krull dimension [Formula: see text]. In this paper, it shown that [Formula: see text] As an application of this result, it is shown that [Formula: see text], for each [Formula: see text] Also it shown that for each [Formula: see text] the submodule [Formula: see text] and [Formula: see text] of [Formula: see text] is [Formula: see text]-cofinite, [Formula: see text] and [Formula: see text] whenever the category of all [Formula: see text]-cofinite [Formula: see text]-modules is an Abelian subcategory of the category of all [Formula: see text]-modules. Also some applications of these results will be included.
Publisher
World Scientific Pub Co Pte Lt
Subject
Applied Mathematics,Algebra and Number Theory
Cited by
2 articles.
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1. A note on cofinite modules over Noetherian complete local rings;Bulletin of the Belgian Mathematical Society - Simon Stevin;2022-12-20
2. On the Abelian categories of cofinite modules;Journal of Algebra and Its Applications;2022-10-04