On (R, S)-Module Homomorphisms

Abstract

Let R and S be arbitrary rings. In the algebraic structure it is known that the R-module structure is a generalization of a vector space. As in the ring structure, in the R-module some previous researchers have defined R-module homomorphisms, the types of R-module homomorphisms, the properties of R-module homomorphisms, and the fundamental theorem of R-module isomorphisms. On the other hand, the R-module structure has been generalized to the (R, S)-module structure. However, research and discussion related to (R, S)-modules are still a bit worked out. Therefore, in this paper we present the definition of (R, S)-module homomorphisms, the types of (R, S)-module homomorphisms, the properties of (R, S)-module homomorphisms, and the fundamental theorem of (R, S)-module isomorphisms.