Article in volume
Authors:
Title:
Strongly regular modules
PDFSource:
Discussiones Mathematicae - General Algebra and Applications 43(1) (2023) 53-62
Received: 2021-04-09 , Revised: 2021-06-23 , Accepted: 2021-06-28 , Available online: 2022-11-29 , https://doi.org/10.7151/dmgaa.1406
Abstract:
The notion of strongly regular modules over a ring which is not necessarily
commutative is introduced. The relation between $F$-regular, $GF$-regular and
$vn$-regular modules that are defined over commutative rings and strongly
regular module is obtained. We have shown that a remark that if $R$ is a reduced
ring, then the $R$-module $M$ is $F$-regular if and only if $M$ is $GF$-regular
is false. We have obtained the necessary and sufficient condition under which
the remark is true. We have shown that if $R$ is a commutative ring and if $M$
is finitely generated multiplication module then the notion of $F$-regular,
$GF$-regular, $vn$-regular and strongly regular are equivalent.
Keywords:
strong $M$-$vn$-regular element, strongly regular module, $F$-regular module, $GF$-reguar module, $vn$-regular module, weak commutative module
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