AN ABELIAN CATEGORY OF WEAKLY COFINITE MODULES

Let I be an ideal of a commutative Noetherian semi-local ring R and M be an R-module. It is shown that if dim M ≤ 2 and SuppR M ⊆ V (I), then M is I-weakly cofinite if (and only if) the R-modules HomR(R/I, M) and Ext1R(R/I, M) are weakly Laskerian. As a consequence of this result, it is shown that t...

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Bibliographic Details
Published in:Taehan Suhakhoe hoebo 2024, Vol.61 (1), p.273-280
Main Author: Gholamreza Pirmohammadi
Format: Article
Language:Korean
Online Access:Get full text
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Summary:Let I be an ideal of a commutative Noetherian semi-local ring R and M be an R-module. It is shown that if dim M ≤ 2 and SuppR M ⊆ V (I), then M is I-weakly cofinite if (and only if) the R-modules HomR(R/I, M) and Ext1R(R/I, M) are weakly Laskerian. As a consequence of this result, it is shown that the category of all I-weakly cofinite modules X with dim X ≤ 2, forms an Abelian subcategory of the category of all R-modules. Finally, it is shown that if dim R/I ≤ 2, then for each pair of finitely generated R-modules M and N and each pair of the integers i, j ≥ 0, the R-modules TorRi(N, HjI(M)) and ExtiR(N, HjI(M)) are I-weakly cofinite.
ISSN:1015-8634