Fundamental Relation on $(m,n)$-Ary Hypermodules Over $(m,n)$-Ary Hyperrings

Abstract

In this paper, the class of $(m,n)$-ary hypermodules is introduced and several properties and examples are found. $(m,n)$-ary hypermodules are a generalization of hypermodules. On the other hand, we can consider $(m,n)$-ary hypermodules as a good generalization of $(m,n)$-ary modules. We define the fundamental relation ${ϵ}^{\ast }$ on the $(m,n)$-ary hypermodules $M$ as the smallest equivalence relation such that $M/{ϵ}^{\ast }$ is an $(m,n)$-ary module, and then some related properties are investigated.