Weakly cofinite模及其局部上同调模的Ext函子的弱Laskerian性

Weakly cofinite modules and weakly Laskerianess of extension functors of local cohomology modules

设(R,m)是Noether局部环,是交换的且有单位元.若模M满足:(i)Supp(M)V(a),(ii)ExtiR(R/a,M)是弱Laskerian的,对所有i≥0,则称M是a-weakly cofin ite的.给出了判定一个模是a-weakly cofin ite的条件,并对ExtiR(R/a,Hta(M))的弱Laskerian性做了讨论(i=0,1,2时).

Let R be a commutative Noether local ring with identity. We say that M is a-weakly coilnite if it satisfies （ i ） Supp （M） lohtain in V（ a ）, （ii） Ext^iR （ R/a, M） is weakly Laskerian for all i≥0. We get a result that when a module is a-weakly cofinite, also we discuss the weakly Laskerianess of Ext^iR （R/a, H^ta（M） ）（i=0,1,2）.