The Research And Properties Of The Associated Prime Ideal

Since the theory of local cohomology is introduced, it has been developed into a very important part of the homological algebra. It is also an useful tool to study the algebraic topology and geometric algebra. In1974, J.Herzog defined the generalized local cohomology modules. Many mathematicians have studied the associated primes of local cohomology modules of weakly Laskerian modules and made a lot of good results. In this thesis, we mainly study the properties of invariants of generalized local cohomology modules of cofinite modules. We also study the finiteness of the associated primes of generalized local cohomology modules of weakly Laskerian modules.Firstly, in order to study the properties of associated primes, we briefly present the basic properties of HI(?)(M,N), the associated primes and the coassociated primes.Secondly, we give a judge method of I-cofiniteness, I-weakly cofiniteness. I-weakly co-cofiniteness. Then we discuss the invariant properties of I-cofiniteness, and whether it is related on SuppR(N). Our main conclusion is that:let R be a ring, M, N, L be finitely generated, and pdM<∞,dim N<∞, if SuppR(L)(?)SuppR(N), then q(I,M,L)≤q(I,M,N).Finally, we study the finiteness of the associated promes of weakly laskerian modules, our main conclusion is that:let R be a ring, r∈N0, M be finitely generated, N be weak laskerian modules, if (?)i<r. H(?)(M,N) be weakly laskeian, L is finitely generated submo-dules of HIr(M,N), then the collection Ass(HIr,(M,N)/L) is finiteness.