Volume 37 • Number 2 • 2014   • The Artinianness of Formal Local Cohomology Modules Yan Gu Abstract. Let I be an ideal of a commutative Noetherian local ring $(R,\frak{m})$, $M$ a finitely generated $R$-module and $\underset{n}{\varprojlim}\, H^i_{\frak{m}}(M/I^nM)$ the $i$-th formal local cohomology module of $M$ with respect to $I$. We prove some results concerning artinianness of $\underset{n}{\varprojlim}\,H^i_{\frak{m}}(M/I^nM)$. We discuss the maximum and minimum integers such that $\underset{n}{\varprojlim}\, H^i_{\frak{m}}(M/I^nM)$ is artinian. 2010 Mathematics Subject Classification: 13D45, 13E10, 13E15 Full text: PDF