A remark on proper sequences of modules

Abstract

A bound for the depth of a quotient of the symmetric algebra, S(E), of a finitely generated module E, over a C.M. ring by an ideal of S(E) generated by a subsequence of x1, . . . , xn is obtained in the case when E satisfies the sliding depth condition, with maximal irrelevant ideal generated by a proper sequence x1, . . . , xn in E