A Study of Noetherian and Artinian (R,S)-Modules

As science develops, a module has been generalized to a new algebraic structure called -module. Some of the concepts in the module can also be extended into the -module structure. The concepts related to the Noetherian module and the Artinian module have never been developed into the -module structure. Therefore, this study aims to examine the development results related to the Noetherian module and the Artinian module in the -module. In this paper, we present the definition of Noetherian -module, the definition of Artinian -module, and the development results of its properties in the -module structure.