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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.
}, issn = {2707-8523}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/cmr/19155.html} }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.