TY  - JOUR
T1  - Quasi regular modules and trivial extension
AU  - Tekir, Ünsal
AU  - Jayaram, Chillumuntala
AU  - Koç, Suat
PY  - 2021
DA  - February
DO  - 10.15672/hujms.613404
JF  - Hacettepe Journal of Mathematics and Statistics
PB  - Hacettepe University
WT  - DergiPark
SN  - 2651-477X
SP  - 120
EP  - 134
VL  - 50
IS  - 1
LA  - en
AB  - 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.
KW  - von Neumann regular rings
KW  - quasi regular rings
KW  - von Neumann regular module
KW  - quasi regular module
KW  - trivial extension
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UR  - https://doi.org/10.15672/hujms.613404
L1  - https://dergipark.org.tr/en/download/article-file/1188049
ER  -