On generalized regular sequences and the finiteness for associated primes of local cohomology modules

摘要

Let (R, m) be a Noetherian local ring and M a finitely generated R-module. The two notions of generalized regular sequence and generalized depth are introduced as extensions of the known notions of regular sequence and depth, respectively. Some properties of generalized regular sequence and generalized depth, which are closely related to those of regular sequence and depth, are given. If x(1),. x(r) is a generalized regular sequence of M, thenboolean ORn1,...nr Ass M/(x(1)(n1),..., x(r)(nr))Mis a finite set. Some finiteness properties for associated primes of local cohomology modules are presented.