Acta Mathematica Sinica, English Series Acta Mathematica Sinica, Published online: June 6, 2018 https://doi.org/10.1007/s10114-018-7461-7 English Series http://www.ActaMath.com Springer-Verlag GmbH Germany & The Editorial Office of AMS 2018 Gang YANG Xuan Shang DA Department of Mathematics, Lanzhou Jiaotong University, Lanzhou 730070,P. R.China E-mail : firstname.lastname@example.org email@example.com Abstract In the paper, Ding projective modules and Ding projective complexes are considered. In particular, it is proven that Ding projective complexes are precisely the complexes X for which each X is a Ding projective R-module for all m ∈ Z. Keywords Gorenstein projective modules, Ding projective and Ding injective modules, Ding projec- tive complexes MR(2010) Subject Classiﬁcation 18G25, 18G35, 55U15, 55U35 1 Introduction In 1966, Auslander introduced the notion of G-dimension of a ﬁnite R-module over a commu- tative noetherian local ring. In 1969, Auslander and Bridger extended this notion to two sided noetherian rings. Calling the modules of G-dimension zero Gorenstein projective modules, in 1995, Enochs and Jenda deﬁned Gorenstein projective (whether ﬁnitely generated or not) and Gorenstein injective modules over an arbitrary ring . Another extension of the G-dimension is based on Gorenstein ﬂat modules. These modules were introduced by Enochs et al. . Gorenstein homological algebra is the relative version
Acta Mathematica Sinica, English Series – Springer Journals
Published: May 31, 2018
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