Abstract

In this paper, the class of $(m,n)$-hyperrings is introduced and several properties are found and examples are presented. $(m,n)$-hyperrings are a generalization of hyperrings. We define the fundamental relation $\Gamma^*$ on an $(m,n)$-hyperring $R$ such that $R/\Gamma^*$ is the smallest $(m,n)$-ring, and then some related properties are investigated.

Keywords: $(m,n)$-hyperring; $n$-ary operation; $n$-ary hyperoperation; $n$-ary hypergroup; fundamental equivalence relation.

MSC: 16Y99

Pages:  1$-$16     

Volume  67 ,  Issue  1 ,  2015