Homomorfisma pada (R,S)-Modul

Ira Lefiana; Suroto Suroto; Ari Wardayani; Najmah Istikaanah

doi:10.37905/euler.v14i2.38237

Homomorfisma pada (R,S)-Modul

Ira Lefiana, Suroto Suroto, Ari Wardayani, Najmah Istikaanah

Abstract

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.

Keywords

Homomorphism; R-module; (R,S)-bimodule; (R,S)-module; quotient (R,S)-module

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DOI: https://doi.org/10.37905/euler.v14i2.38237