Local Cohomology Modules Of Weakly Laskerian Modules

Local cohomology is an important tool in studying algebraic geometry and algebraic topology.Many scholars have been absorbed in studying it and have made some effort to develop it.Many scholars have been studyed on local cohomology moules of finitely generated modules.In 2005,Divaani-Aazar and Mafi defined weakly Laskerian modules as a generalization of finitely generated modules.In this paper,we mainly study the associated primes,weakly cofiniteness of local cohomology modules of weakly Laskerian modules.Also we study the depth of weakly Laskerian modules.Firstly,we recall some basic concepts,preliminary results and some famous theorems about them,which will be probably used in this paper.Secondly,we mainly study the finiteness of the set of associated prime ideals of local cohomology modules about weakly Laskerian modules.Our mainly result is that:let M is a weakly Laskerian module,i is a non-negative integer,then the set of associated primes of H_Iⁱ(M)is a finite set,if one of the following conditions is true:(α)Supp(H_I^j(M))is a finite set,(?)j＜i;(β)H_I^j(M)is finitely generated,(?)j＜i.Next,we study the depth of weakly Laskerian modules.It's shown that when M is a weakly Laskerian module,the I-depth of M,depth(I,M)is equal to inf{r∈N₀|H_I^r(M)≠0}.At last,we study the weakly cofiniteness of lacal cohomology modules about weakly Laskerian modules.We give a result about the weakly cofiniteness of local cohomology modules,which generalize the mainly result of[6].