On Ding Projective Complexes

On Ding Projective Complexes 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 : yanggang@mail.lzjtu.cn 157834354@qq.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 [11]. Another extension of the G-dimension is based on Gorenstein flat modules. These modules were introduced by Enochs et al. [13]. Gorenstein homological algebra is the relative version http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Acta Mathematica Sinica, English Series Springer Journals

On Ding Projective Complexes

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Publisher
Springer Journals
Copyright
Copyright © 2018 by Institute of Mathematics, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Chinese Mathematical Society and Springer-Verlag GmbH Germany, part of Springer Nature
Subject
Mathematics; Mathematics, general
ISSN
1439-8516
eISSN
1439-7617
D.O.I.
10.1007/s10114-018-7461-7
Publisher site
See Article on Publisher Site

Abstract

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 : yanggang@mail.lzjtu.cn 157834354@qq.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 [11]. Another extension of the G-dimension is based on Gorenstein flat modules. These modules were introduced by Enochs et al. [13]. Gorenstein homological algebra is the relative version

Journal

Acta Mathematica Sinica, English SeriesSpringer Journals

Published: May 31, 2018

References

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