Document Type : Original Manuscript


Faculty of Mathematical Sciences and Computer, Kharazmi University, P.O. Box 1561836314, 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.


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