## Quasi regular modules and trivial extension

HACETTEPE JOURNAL OF MATHEMATICS AND STATISTICS, vol.50, no.1, pp.120-134, 2021 (Peer-Reviewed Journal)

• Publication Type: Article / Article
• Volume: 50 Issue: 1
• Publication Date: 2021
• Doi Number: 10.15672/hujms.613404
• Journal Name: HACETTEPE JOURNAL OF MATHEMATICS AND STATISTICS
• Journal Indexes: Science Citation Index Expanded, Scopus, zbMATH
• Page Numbers: pp.120-134
• Keywords: von Neumann regular ring, quasi regular ring, von Neumann regular module, quasi regular module, trivial extension

#### Abstract

Recall that a ring R is said to be a quasi regular ring if its total quotient ring q(R) is von Neumann regular. It is well known that a ring R is quasi regular if and only if it is a reduced ring satisfying the property: for each a is an element of R, ann(R)(ann (R) (a)) = ann(R)(b) for some b is an element of R. Here, in this study, we extend the notion of quasi regular rings and rings which satisfy the aforementioned property to modules. We give many characterizations and properties of these two classes of modules. Moreover, we investigate the (weak) quasi regular property of trivial extension.