TY - JOUR T1 - Some Results for Formal Local Cohomology Modules AU - Chu , Lizhong JO - Communications in Mathematical Research VL - 3 SP - 230 EP - 238 PY - 2021 DA - 2021/05 SN - 26 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/cmr/19155.html KW - local cohomology, formal local cohomology, coartinian module, minimax module, Artinian module. AB -

Let $(R, m)$ be a commutative Noetherian local ring, $I$ an ideal of $R$ and $M$ a finitely generated $R$-module. Let $\mathop{\rm lim}\limits_{\mathop{n} \limits ^{\longleftarrow}}H^i_m(M/I^nM)$ be the $i$th formal local cohomology module of $M$ with respect to $I$. In this paper, we discuss some properties of formal local cohomology modules $\mathop{\rm lim}\limits_{\mathop{n} \limits ^{\longleftarrow}}H^i_m(M/I^nM)$, which are analogous to the finiteness and Artinianness of local cohomology modules of a finitely generated module.