(n, m)-STRONGLY GORENSTEIN PROJECTIVE MODULES

Authors : Driss BENNİS

Pages : 119-133

View : 17 | Download : 10

Publication Date : 2009-12-01

Article Type : Research Paper

Abstract :This paper is a continuation of the papers J. Pure Appl. Algebra, 210 insert ignore into journalissuearticles values(2007);, 437–445 and J. Algebra Appl., 8 insert ignore into journalissuearticles values(2009);, 219–227. Namely, we introduce and study a doubly filtered set of classes of modules of finite Gorenstein projective dimension, which are called insert ignore into journalissuearticles values(n, m);-strongly Gorenstein projective insert ignore into journalissuearticles values(insert ignore into journalissuearticles values(n, m);-SG-projective for short);insert ignore into journalissuearticles values(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 insert ignore into journalissuearticles values(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.
Keywords : Gorenstein projective modules, Gorenstein projective dimension, n, strongly Gorenstein projective modules, n, m, SG projective modules