1
Departmen of Mathematics, Zanjan Branch, Islamic Azad University, Zanjan, Iran.
2
Department of Mathematics, Mobarakeh Branch, Islamic Azad University, Isfahan, Iran.
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.
Fathi, A., & Hajikarimi, A. (2024). On the finiteness of local homology modules. Journal of Algebraic Systems, (), -. doi: 10.22044/jas.2023.12118.1631
MLA
Ali Fathi; Alireza Hajikarimi. "On the finiteness of local homology modules". Journal of Algebraic Systems, , , 2024, -. doi: 10.22044/jas.2023.12118.1631
HARVARD
Fathi, A., Hajikarimi, A. (2024). 'On the finiteness of local homology modules', Journal of Algebraic Systems, (), pp. -. doi: 10.22044/jas.2023.12118.1631
VANCOUVER
Fathi, A., Hajikarimi, A. On the finiteness of local homology modules. Journal of Algebraic Systems, 2024; (): -. doi: 10.22044/jas.2023.12118.1631