Abstract:Let ${\frak{a}}$ be an ideal of Noetherian local ring $(R,{\frak{m}})$ and $M$ a finitely generated $R$-module of dimension $d$. In this paper we investigate the Artinianness of formal local cohomology modules under certain conditions on the local cohomology modules with respect to ${\frak{m}}$. Also we prove that for an arbitrary local ring $(R,{\frak{m}})$ (not necessarily complete), we have ${\rm Att}_R(\mathfrak{F}_{\frak{a}}^d(M)) ={\rm Min} {\rm V}({\rm Ann}_R \mathfrak{F}_{\frak{a}}^d(M)).$
Keywords: formal local cohomology; local cohomology
DOI: DOI 10.14712/1213-7243.2019.006
AMS Subject Classification: 13D45 13E99