Category of Generalized Modules Over Two Different Rings

Abstract

In this paper,a method of enriched category theory to form a closed symmetricmonoidal structure on the category of generalized modules CR= (modR,Ab) have been implemented. Further, a new kind of generalized module category defined on two commutativerings R and S, denoted by CRS = (modR,modS) is constructed.Finally, the authors studied a localization on this type of categories, both of them are Grothendieck