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• W2964157094 abstract "This paper generalize the idea of the authors in (2). Namely, we define and study a particular case of modules with Gorenstein projective, injective, and flat dimension less or equal than n � 0 , which we call, re- spectively, strongly n-Gorenstein projective, injective and flat modules. These three classes of modules give us a new characterization of the first modules, and they are a generalization of the notions of strongly Gorenstein projective, injective, and flat modules respectively. Throughout this paper, all rings are commutative with identity element, and all modules are unital. Let R be a ring, and let M be an R-module. As usual we use pd R(M), id R(M) and fd R(M) to denote, respectively, the classical projective dimension, injective dimension and flat dimension of M. By gldim(R) and wdim(R) we denote, respec- tively, the classical global dimension and weak dimension of R. It is convenient to use local to refer to (not necessarily Noetherian) rings with a unique maximal ideal. For a two-sided Noetherian ring R, Auslander and Bridger (1) introduced the G-dimension, Gdim R(M), for every finitely generated R-module M. They proved the inequality Gdim R(M) ≤ pd R(M) with equality Gdim R(M) = pd R(M) when pd R(M) is finite. Several decades later, Enochs and Jenda (9, 10) defined the notion of Gorenstein projective dimension (G-projective dimension for short), as an extension of G- dimension to modules that are not necessarily finitely generated, and the Gorenstein injective dimension (G-injective dimension for short) as a dual notion of Gorenstein projective dimension. Then, to complete the analogy with the classical homolog- ical dimension, Enochs, Jenda and Torrecillas (11) introduced the Gorenstein flat dimension. Some references are (6, 7, 9, 10, 11). In 2004, Holm (13) generalized several results which are already obtained over Noetherian rings to associative rings. Recently in (3), the authors started the study of global Gorenstein dimensions of rings, which are called, for a commutative ring R, projective, injective, and weak dimensions of R, denoted by GP D(R), GID(R), and G.wdim(R), respectively, and, respectively, defined as follows:" @default.
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• W2964157094 date "2009-04-01" @default.
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• W2964157094 title "Strongly $n$-Gorenstein projective, injective and flat modules" @default.
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