- Hacettepe Journal of Mathematics and Statistics
- Vol: 50 Issue: 1
- Quasi regular modules and trivial extension
Quasi regular modules and trivial extension
Authors : Chillumuntala Jayaram, Ünsal Tekir, Suat Koç
Pages : 120-134
Doi:10.15672/hujms.613404
View : 14 | Download : 8
Publication Date : 2021-02-04
Article Type : Research
Abstract :Recall that a ring $R\ $is said to be a quasi regular ring if its total quotient ring $q(R)\ $is \textit{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 $a\in R,$ $ann_{R}(ann_{R}(a))=ann_{R}(b)$ for some $b\in R$. 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.Keywords : von Neumann regular rings, quasi regular rings, von Neumann regular module, quasi regular module, trivial extension