GIac-内射模与GIac-平坦模的环刻画

兰州理工大学学报 ›› 2021, Vol. 47 ›› Issue (3): 156-161.

GI_ac-内射模与GI_ac-平坦模的环刻画

陈东^*

成都大学信息科学与工程学院, 四川成都 610106

收稿日期:2020-06-18 出版日期:2021-06-28 发布日期:2021-07-19
通讯作者: 陈东(l983-),男,四川成都人,硕士,讲师.Email:chendong@cdu.edu.cn
基金资助:
国家自然科学基金(1167l283),四川省教育厅基金(l8ZB0l38),四川省高校重点实验室开放基金(MSSB-2020-06)

Ring characterizations on GI_ac- injective and GI_ac-flat modules

CHEN Dong

College of information science and engineering, Chengdu University, Chengdu 610106, China

Received:2020-06-18 Online:2021-06-28 Published:2021-07-19

摘要/Abstract

摘要： 引入GI_ac-内射模和GI_ac-平坦模的概念,是介于GI-内射模(或 GI-平坦模)与余纯内射模(或余纯平坦模)之间的一种模类.用上述模刻画了诸多环类,如:半单环、von Neumann 正则环、遗传环和半遗传环.

关键词: GI_ac-内射模, GI_ac-平坦模, 半单环, von Neumann 正则环, (半)遗传环

Abstract: The concept of GI_ac-injective modules and GI_ac-flat modules , is introduced respectively, which is a class of modules between GI-injective modules (or GI-flat modules) and copure injective modules (or copure flat modules). Some classes of rings, such as semisimple rings, von Neumann regular rings, hereditary rings and semihereditary rings, are characterized in terms of these modules.

Key words: GI_ac-injective modules, GI_ac-flat modules, semisimple rings, von Neumann regular rings, (semi)hereditary rings

中图分类号:

O154

陈东. GI_ac-内射模与GI_ac-平坦模的环刻画[J]. 兰州理工大学学报, 2021, 47(3): 156-161.

CHEN Dong. Ring characterizations on GI_ac- injective and GI_ac-flat modules[J]. Journal of Lanzhou University of Technology, 2021, 47(3): 156-161.

参考文献

[1] GAO Z H.On GI-injective Modules [J].Communications in Algebra,2012,40(10):3841-3858.
[2] GAO Z H.On GI-flat modules and dimensions [J].Journal of the Korean Mathematical Society,2013,50(1):203-218.
[3] PAN Q,ZHU X.GP-projective and GI- injective modules [J].Mathematical Notes,2012,91(5/6):824-832.
[4] 王修建,赵玉娥,杜先能.关于GI-平坦模和GF-挠模 [J].中国科学技术大学学报,2015,45(3):193-198.
[5] ZHAO T,XU Y.On right orthogonal classes and cohomology over ding-chen rings [J].Bulletin of the Malaysian Mathematical Sciences Society,2017,40(2):617-634.
[6] BRAVO D,GILLESPIE J.Absolutely clean,level,and Gorenstein AC-injective complexes[J].Communications in Algebra,2014,44(5):2213-2233.
[7] BRAVO D,PEREA M.Finiteness conditions and cotorsion pairs [J].Journal of Pure and Applied Algebra,2017,221(6):1249-1267.
[8] JAMES G.AC-Gorenstein rings and their stable categories[J].Journal of the Australian Mathematical Society,2019,107(2):181-198.
[9] BRAVO D,GILLESPIE J,HOVEY M.The stable module category of a general ring [J/OL].Cornell University Library.[2014-05-22].http://arxiv.org/pdf/1405.5768v1.pdf.
[10] BRAVO D,ESTRADA S,IACOB A.FP_n-injective,FP_n-flat covers and preenvelopes,andGorenstein AC-flat covers [J].Algebra Colloquium,2018,25(2):319-334.
[11] GAO Z,WANG F.Weak injective and weak flat modules [J].Communications in Algebra,2015,43(9):3857-3868.
[12] GAO Z,HUANG Z.Weak injective covers and dimension of modules [J].Acta Mathematica Hungarica,2015,147(1):135-157.
[13] ZHAO T.Homological properties of modules with finite weak injective and weak flat dimensions [J].Bulletin of the Malaysian Mathematical Sciences Society,2017,41(2):1-27.
[14] 陈东,熊涛.关于Gorenstein AC-余挠模 [J].安徽大学学报(自然科学版),2020,44(5):35-40.
[15] BENNIS D,MAHDOU N.Strongly Gorenstein projective,injective,and flat modules [J].Journal of Pure and Applied Algebra,2007,210(2):437-445.
[16] DING N,CHEN J.The flat dimensions of injective modules [J].Manuscripta Math,1993,78(1):165-177.