Some Results on the Soft Crossed Polymodules

Abstract

‎In this paper‎, ‎we introduce the concept of soft polyaction and establish some characterizations about it‎. ‎Moreover‎, ‎we introduce the concepts of stabilizer‎, ‎normalizer‎, ‎and centralizer related to soft polyaction‎, ‎and the relationship between them‎, ‎then give examples of them‎.

‎Our most important goal in this paper is to investigate the semi-direct product of soft polygroups and Cayley's theorem for soft polygroups and to reach the definition of soft crossed polymodules‎. ‎In fact‎, ‎expanding the concepts of group theory in algebraic hyperstructures is one of the most important goals of the article‎. ‎By defining soft crossed polymodules‎, ‎the research method of researchers in this topic is determined from the theory of algebraic hyperstructures‎.