Strongly regular modules

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.