The Properties Of Associated Primes Of Local Cohomology Modules

Along with the development of algebra, homology algebra, as an important subfield, gradually plays an important role in other subfields since its introduction. Local cohomology theory,which is extended form the homology algebra,is attracting more and more scholars attention.Many properties of local cohomology modules are right only when their associated primes are finite.So problems like when the associated primes of the local cohomology modules are finite, whether there is finite minimum associated primes if the number of the associated primes are finite, etc, are researched more and more by many scholars on modern commutative algebraand homology algebra.This article discusses the properties of associated promes of local cohomology modules on the basis of many researches about the associated promes of local cohomology modules:Firstly, we introduce some basic concepts and their properties,including some theorems;Secondly, in order to research on the properties of cofinite modules, weakly Laskerian modules and weakly cofinite modules, we first discuss the relations of Spec(R), SuppR (M), AssR (M) and AnnR (M). Thirdly, some properties of local cohomology modules are given,then we are discussing some properties and theorem based on the properties of cofinite modules.Next we continue to study the finiteness of cofinite modules based on the properties of weakly Laskerian modules.Finally, by understanding the properties of associated primes of cofinite modules and weakly Laskerian modules,we research further on the properties of associated primes of weakly cofinite modules.