Homomorfisma pada (R,S)-Modul - Ira Lefiana; Suroto Suroto; Ari Wardayani; Najmah Istikaanah (Euler : Jurnal Ilmiah Matematika, Sains dan Teknologi, 2026)
The (R,S)-module structure is a generalization of the (R,S)-bimodule structure. The (R,S)-bimodule structure itself is an extension of the R-module structure. Thus, some properties that apply to R-modules can be extended to (R,S)-modules. In this article, we discuss the (R,S)-module homomorphism and its properties. The method used is to add a ring S action on the right to the R-module homomorphism and extend the compatibility condition to the (R,S)-bimodule homomorphism. The result is that the (R,S)-module homomorphism can be constructed from the R-module homomorphism by adding a ring S action from the right and extending the compatibility condition to the (R,S)-bimodule homomorphism with the associative condition of simultaneous action to obtain the left-linear and right-linear conditions simultaneously on the (R,S)-module homomorphism. Furthermore, the kernel and image structures as (R,S)-submodules and (R,S)-factor module structures must also maintain the consistency of the left action of the ring R as well as the right action of the ring S simultaneously.