(n, m)-Strongly Gorenstein Projective Modules

This paper is a continuation of the papers J. Pure Appl. Algebra, 210 (2007), 437–445 and J. Algebra Appl., 8 (2009), 219–227. Namely, we introduce and study a doubly filtered set of classes of modules of finite Gorenstein projective dimension, which are called (n, m)-strongly Gorenstein projective ((n, m)-SG-projective for short) for integers n ≥ 1 and m ≥ 0. We are mainly interested in studying syzygies of these modules. As consequences, we show that a module M has Gorenstein projective dimension at most m if and only if M ⊕G is (1, m)-SG-projective for some Gorenstein projective module G. And, over rings of finite left finitistic flat dimension, that a module of finite Gorenstein projective dimension has finite projective dimension if and only if it has finite flat dimension.