Given a module M over a ring R that has a grading by a semigroup Q, we present a spectral sequence that computes the local cohomology H I(M) at any graded ideal I in terms of Ext modules. We use this method to obtain finiteness results for the local cohomology of graded modules over semigroup rings. In particular we prove that for a semigroup Q whose saturation Q is simplicial, and a finitely g...

Let (R,m) be a local Noetherian ring, let I ⊂ R be any ideal and let M be a finitely generated R-module. It has been long conjectured that the local cohomology modules H I(M) have finitely many associated primes for all i (see Conjecture 5.1 in [H] and [L].) If R is not required to be local these sets of associated primes may be infinite, as shown by Anurag Singh in [S], where he constructed an...

let a be a banach algebra. a is called ideally amenable if for every closed ideal i of a, the first cohomology group of a with coefficients in i* is trivial. we investigate the closed ideals i for which h1 (a,i* )={0}, whenever a is weakly amenable or a biflat banach algebra. also we give some hereditary properties of ideal amenability.

Auslander’s depth formula for pairs of Tor-independent modules over a regular local ring, depth(M ⊗R N) = depth M + depth N − depthR, has been generalized in several directions; most significantly it has been shown to hold for pairs of Tor-independent modules over complete intersection rings. In this paper we establish a depth formula that holds for every pair of Tate Tor-independent modules ov...

‎In this article we introduce $mu$-filtered fuzzy module with a family of fuzzy submodules.  It shows the relation between $mu$-filtered fuzzy modules and crisp filtered modules by level sets. We investigate fuzzy topology on the $mu$-filtered fuzzy module and apply that to introduce fuzzy completion. Finally we extend Krull's intersection theorem of fuzzy ideals by using concept $mu$-adic comp...