The construction of fractions of $\Gamma$-module over commutative $\Gamma$-ring

Abstract

The aim of this paper is to construct fraction of $\Gamma$-module over commutative $\Gamma$-ring. There should be an appropriate set $S$ of elements in a $\Gamma$-ring $R$ to be used as $\Gamma$-module of fractions. Then we study the homomorphisms of $\Gamma$-module which can lead to related basic results. We show that for every $\Gamma$-module $M$, $S^{-1}(0:_R M)=(0:_{S^{-1}R} S^{-1}M).$ Also, if $M$ is a finitely generated $R_\Gamma$-module, then $S^{-1}M$ is finitely generated.

Keywords

• gamma ring of fraction
• gamma module of fraction
• finitely generated gamma module