On Right Orthogonal Classes and Cohomology Over Ding–Chen Rings

In this paper, we investigate the properties of right orthogonal modules of C , where C is a class of left R -modules. As an application, we investigate the properties of right orthogonal modules of Ding injective left R -modules, and present various characterizations of semisimple and von Neumann r...

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Bibliographic Details
Published inBulletin of the Malaysian Mathematical Sciences Society Vol. 40; no. 2; pp. 617 - 634
Main Authors Zhao, Tiwei, Xu, Yunge
Format Journal Article
LanguageEnglish
Published Singapore Springer Singapore 01.04.2017
Springer Nature B.V
Subjects
Applications of Mathematics
Mathematics
Mathematics and Statistics
Modules
Rings (mathematics)
Strong Tate cohomology
16E30
16E10
16E60
flat module
Von Neumann regular ring
injective module
Semisimple ring
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Summary:In this paper, we investigate the properties of right orthogonal modules of C , where C is a class of left R -modules. As an application, we investigate the properties of right orthogonal modules of Ding injective left R -modules, and present various characterizations of semisimple and von Neumann regular rings and so on. Moreover, we also consider another cohomology, strong Tate cohomology, which connects the usual cohomology with the Ding cohomology.
ISSN:0126-6705
2180-4206
DOI:10.1007/s40840-017-0461-4