Geodesic
Strongly regular modules
Discussiones Mathematicae. General Algebra and Applications, Tome 43 (2023) no. 1, pp. 53-62

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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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Sudharshana, Govindarajulu Narayanan; Sivakumar, Duraisamy. Strongly regular modules. Discussiones Mathematicae. General Algebra and Applications, Tome 43 (2023) no. 1, pp. 53-62. http://geodesic.mathdoc.fr/item/DMGAA_2023_43_1_a4/