全部 标题 作者
关键词 摘要

OALib Journal期刊
ISSN: 2333-9721
费用：99美元
投递稿件

查看量下载量

相关文章

更多...

投射余可解的Gorenstein平坦模和Gorenstein AC投射模
Projectively Coresolved Gorenstein Flat Modules and Gorenstein AC Projective Modules

DOI: 10.12677/PM.2021.114074, PP. 606-611

Keywords: 投射余可解的Gorenstein平坦模，Gorenstein AC投射模，Gorenstein投射模
Projectively Coresolved Gorenstein Flat Module, Gorenstein AC Projective Module, Gorenstein Projective Module

Full-Text   Cite this paper   Add to My Lib

Abstract:

本文我们给出了Gorenstein AC投射模的类与投射余可解的Gorenstein平坦模的类等价的条件，证明了在凝聚环R上，Gorenstein AC投射模的类，投射余可解的Gorenstein平坦模的类与Ding投射模的类等价。同时也给出了Gorenstein AC投射模的类与Gorenstein投射模的类等价的充分必要条件，证明了在任意环R上，Gorenstein AC投射模的类与Gorenstein投射模的类等价当且仅当Level模的类包含在Gorenstein投射模的类的右正交中。最后我们给出了Gorenstein AC投射模的类与Gorenstein投射模的类在凝聚环上等价的一些充分必要条件。
In this paper, we give a condition in order for the class of Gorenstein AC projective modules to co-incide with the class of projectively coresolved Gorenstein flat modules, we prove that the class of Gorenstein AC projective modules equal to the class of projectively coresolved Gorenstein flat modules equal to the class of Ding projective modules over coherent rings. We also give a necessary and sufficient condition in order for the class of Gorenstein AC projective modules to coincide with the class of Gorenstein projective modules, we prove that the class of Gorenstein AC projective modules to coincide with the class of Gorenstein projective modules if and only if the class of level modules belongs to the right orthogonal class with respect to Gorenstein projective modules. And we give some necessary and sufficient conditions in order for the class of Gorenstein AC projective modules to coincide with the class of Gorenstein projective modules over coherent rings.

References

[1]  Enochs, E.E. and Jenda, O.M.G. (1995) Gorenstein Injective and Gorenstein Projective Modules. Mathematische Zeitschrift, 220, 611-633.
https://doi.org/10.1007/BF02572634
[2]  Enochs, E.E., Jenda, O.M.G. and Torrecillas, B. (1993) Gorenstein Flat Modules. Annals of Mathematics, Nanjing University, 10, 1-9.
[3]  Ding, N., Li, Y. and Mao, L. (2009) Strongly Gorenstein Flat Modules. Journal of the Australian Mathematical Society, 86, 323-338.
https://doi.org/10.1017/S1446788708000761
[4]  Gillespie, J. (2010) Model Structures on Modules over Ding-Chen Rings. Homology, Homotopy and Applications, 12, 61-73.
https://doi.org/10.4310/HHA.2010.v12.n1.a6
[5]  Gillespie, J. (2015) On Ding Injective, Ding Projective, and Ding Flat Modules and Complexes. Rocky Mountain Journal of Mathematics, 47, 2641-2673.
[6]  Saroch, J. and Stovícek, J. (2020) Singular Compactness and Definability for ？-Cotorsion and Gorenstein Modules. Selecta Mathematica, 26, 23-63.
https://doi.org/10.1007/s00029-020-0543-2
[7]  Iacob, A. (2020) Projectively Coresolved Gorenstein Flat and Ding Projective Modules. Communications in Algebra, 48, 2883-2893.
https://doi.org/10.1080/00927872.2020.1723612
[8]  Bravo, D., Gillespie, J. and Hovey, M. (2014) The Stable Module Category of a General Ring. Mathematics, arxiv: 1210.0196.
[9]  Holm, H. (2004) Gorenstein Homological Dimensions. Journal of Pure and Applied Algebra, 189, 167-193.
https://doi.org/10.1016/j.jpaa.2003.11.007
[10]  Gillespie, J. (2018) Gorenstein AC-Projective Complexes. Journal of Homotopy and Related Structures, 13, 769-791.
https://doi.org/10.1007/s40062-018-0203-9
[11]  Emmanouil, I. (2012) On the Finiteness of Gorenstein Homo-logical Dimensions. Journal of Algebra, 372, 376-396.
https://doi.org/10.1016/j.jalgebra.2012.09.018
[12]  Estrada, S., Iacob, A. and Pérez, M. (2017) Model Structures and Relative Gorenstein Flat Modules and Chain Complexes. Contemporary Mathematics, arxiv: 1709.00658.

Full-Text

Contact Us

service@oalib.com

QQ:3279437679

WhatsApp +8615387084133