Đang chuẩn bị liên kết để tải về tài liệu:
The Ext-strongly Gorenstein projective modules

In this paper, we introduce and study Ext-strongly Gorenstein projective modules. We prove that the class of Ext-strongly Gorenstein projective modules is projective resolving. Moreover, we consider Ext-strongly Gorenstein projective precovers. | Turkish Journal of Mathematics http://journals.tubitak.gov.tr/math/ Research Article Turk J Math (2015) 39: 54 – 62 ¨ ITAK ˙ c TUB ⃝ doi:10.3906/mat-1405-37 The Ext-strongly Gorenstein projective modules Jie REN∗ Audio-visual Center, The Nanjing Institute of Tourism and Hospitality, Nanjing, Jiangsu, P.R. China Received: 13.05.2014 • Accepted: 06.08.2014 • Published Online: 19.01.2015 • Printed: 13.02.2015 Abstract: In this paper, we introduce and study Ext-strongly Gorenstein projective modules. We prove that the class of Ext-strongly Gorenstein projective modules is projective resolving. Moreover, we consider Ext-strongly Gorenstein projective precovers. Key words: Strongly Gorenstein projective modules, precovers, Ext-strongly Gorenstein projective modules, projectively resolving 1. Introduction Throughout this paper, all rings considered are associative with identity 1 unless otherwise specified and all modules will be unitary. By P(R) we denote the classes of all projective R -modules. For an R -module M , we use pdR (M ) to denote the usual projective dimensions of M . Recall that a class X of R -modules is called resolving if P(R) ⊆ X and for every short exact sequence 0 → X ′ → X → X ′′ → 0 with X ′′ ∈ X the conditions X ′ ∈ X and X ∈ X are equivalent. The notion of a resolving class was introduced by Auslander and Bridger [1] in the studying of G- dimension zero modules in 1969. The G-dimension has strong parallels to the projective dimension. Enochs and Jenda [9,10] extended the ideas of Auslander and Bridger, and introduced Gorenstein projective dimensions, which have all been studied extensively by their founders and by Avramov, Christensen, Foxby, Frankild, Holm, Martsinkovsky, and Xu among others [2,7,8,11–13,15] over arbitrary associative rings. Bennis and Mahdou [4] studied a particular case of Gorenstein projective modules, which they call strongly Gorenstein projective (SG -projective for short) modules. They proved that every .