On the annihilators of generalized local cohomology modules

Let {\frak{a}} be an ideal of Noetherian  ring R and M, N be two finitely generated  R-modules. In this paper, we obtain some results about  the annihilators of  top generalized local cohomology modules.  We define T:=T_R(\frak{a},M, N) as the largest submodule of N such that\\ cd(\frak{a},M, T_R(\frak{a},M,N))<\operatorname{cd}(\frak{a},M,N). Let   (R,\frak{m}) be  a  complete Gorenstein Noetherian local  ring such that pd(M)=d<\infty, dim\  N=dim\ R=n<\infty and   cd(\frak{a},M,N)=d+n. We prove that if  Ass_R(Ext_R^d(M,N/T))\subseteq Ass_R R, then     Ann_R(H_{\frak{m}}^{d+n}(M,N))\subseteq Ann_R Ext_R^d(M,N/T).

کلیدواژه ها:

Annihilator ، local cohomology ، generalized local cohomology