A Generalization of Formal Local Cohomology Modules

Abstract

. Let a and b be two ideals of a commutative Noetherian ring R , M a (cid:12)nitely generated R -module and i an integer. In this paper we study formal local cohomology modules with respect to a pair of ideals. We denote the i -th a -formal local cohomology module M with respect to b by F i a ; b ( M ). We show that if F i a ; b ( M ) is artinian, then a (cid:18) √ (0 : F i a ; b ( M )). Also, we show that F dim M a ; b ( M ) is artinian and we determine the set Att R F dim M a ; b ( M ).