Artinianness and Attached Primes of Formal Local Cohomology Modules

Abstract

Let 𝔞 be an ideal of a local ring (R, 𝔪) and M a finitely generated R-module. In this paper we study the Artinianness properties of formal local cohomology modules and we obtain the lower and upper bounds for Artinianness of formal local cohomology modules. Additionally, we determine the set [Formula: see text] and we show that the set of all non-isomorphic formal local cohomology modules [Formula: see text] is finite.