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 \(\epsilon^*\) on the \((m,n)\)-ary hypermodules \(M\) as the smallest equivalence relation such that \(M/\epsilon^*\) is an \((m,n)\)-ary module, and then some related properties are investigated.