On $(m,n)$-ary $P$-$H_{v}$-modules and their isomorphism theorems

Document Type : Original Manuscript

Authors

1 Abu Dhabi University

2 Yazd University

10.22044/jas.2023.12904.1703

Abstract

After introducing the definition of hypergroups by Marty, the study of hyperstructures and its generalization to $(m,n)$-ary hyperstructures has been of great importance. In this paper, we construct the structure of $(m,n)$-ary $H_v$-modules over $(m,n)$-ary $H_v$-rings by using the notion of $P$-hyperoperations. We study their properties and prove their isomorphism theorems.

Keywords