… If Y⊂ Spec R is a locally closed subset and M is an R -module, we denote by H Y i (R) the i
th local cohomology module … The following properties of modules of the form T(R) are known: …

… Noetherian ring with non-zero identity, a and b ideals of R with a ⊆ b, and M a finitely
generated R-module. In this paper, for fixed integers j and n, we study the finiteness of Extj …

… In this paper, we provide connections between finiteness property of generalized local
cohomology modules and that of ordinary local cohomology modules. To do this, we prove the …

… of generalized local cohomology and usual local cohomology modules and then obtain …
recall briefly definitions and basic properties of weakly Laskerian modules that we shall use. …

… The finiteness properties of generalized local cohomology modules are not well
understood, too. Recently, in [20, 2.8], it is shown that, for any nonzero principal ideal I of R …

… the formal local cohomology modules , i ≥ … finiteness properties of formal local cohomology
modules which indicate that these modules behave very similar to local cohomology modules…

… However, they frequently have properties that make them manageable objects of study. …
finiteness properties. In the first chapter we will study the local cohomology functors for modules …

… modules M and N was introduced by Herzog in [10]. Clearly, it is a generalization of the usual
local cohomology module… On the finiteness properties of the generalized local cohomology …

… By taking (co-)homology we get the finiteness of µi(m,M) and βi(m,M) for all i. In case dim
Supp M > 0, consider the exact sequence 0 → L → M → M → 0, where L = Γm(M) and M = M/L. …

… The purpose of this article is to introduce the notation of the nth finiteness dimension for all n
… For an R-module M, the ith local cohomology module of M with support in V(I) is defined as: …