Some Results for Formal Local Cohomology Modules (Communications in Mathematical Research, 2021)
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 propertiesof formal local cohomology modules $\mathop{\rm lim}\limits_{\mathop{n} \limits ^{\longleftarrow}}H^i_m(M/I^nM)$, which are analogous to thefiniteness and Artinianness of local cohomology modules of a finitely generated module.
Keywords: local cohomology; formal local cohomology; coartinian module; minimax module; Artinian module.