(n,m)-Strongly Gorenstein Projective Modules

Abstract

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 $n\ge 1$ and $m\ge 0$. 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 $M\oplus G$ 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.

to appear in International Electronic Journal of Algebra

References in corpus (1)

• Global Gorenstein dimensions of polynomial rings and of direct product of rings