@article {
author = {Fathi, Ali and Hajikarimi, Alireza},
title = {ON THE FINITENESS OF LOCAL HOMOLOGY MODULES},
journal = {Journal of Algebraic Systems},
volume = {},
number = {},
pages = {-},
year = {2024},
publisher = {Shahrood University of Technology},
issn = {2345-5128},
eissn = {2345-511X},
doi = {10.22044/jas.2023.12118.1631},
abstract = {Let $R$ be a commutative Noetherian ring and $\mathfrak{a}$ be an ideal of $R$. Suppose $M$ is a finitely generated $R$-module and $N$ is an Artinian $R$-module. We define the concept of filter coregular sequence to determine the infimum of integers $i$ such that the generalized local homology $\textrm{H}^{\mathfrak{a}}_i(M, N)$ is not finitely generated as an $\widehat{R}^{\mathfrak{a}}$-module, where $\widehat{R}^{\mathfrak{a}}$ denotes the $\mathfrak{a}$-adic completion of $R$. In particular, if $R$ is a complete semi-local ring, then $\textrm{H}^{\mathfrak{a}}_i(M, N)$ is a finitely generated $\widehat{R}^{\mathfrak{a}}$-module for all non-negative integers $i$ if and only if $(0:_N\mathfrak{a}+\textrm{Ann}(M))$ has finite length.},
keywords = {local homology,Tor functor,finiteness,filter coregular sequence},
url = {https://jas.shahroodut.ac.ir/article_3096.html},
eprint = {https://jas.shahroodut.ac.ir/article_3096_ebdecf06945b4a8979309c94013e9701.pdf}
}