A. Ghanbari Doust - Faculty of Mathematical Sciences and Computer, Kharazmi University, P.O. Box ۱۵۶۱۸۳۶۳۱۴, Tehran, Iran.

Let a be a proper ideal of a ring R. A finitely generated R-module M is said to be a-relative generalized Cohen-Macaulay if f_a (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.

cohomological dimension, finiteness dimension, relative generalized Cohen-Macaulay