A NOTE ON RELATIVE GENERALIZED COHEN-MACAULAY MODULES

Let a be a proper ideal of a ring R. A finitely generated R-module M is said to be a-relative generalized CohenMacaulay if fa(M) = cd(a,M). In this note, we introduce a suitable notion of length of a module to characterize the above mentioned modules. Also certain syzygy modules over a relative Cohen-Macaulay ring are studied.