Constructions of (m,n)-hyperrings

Abstract

In this paper, the class of $(m,n)$-hyperrings is introduced andseveral properties are found and examples are presented.$(m,n)$-hyperrings are a generalization of hyperrings. We definethe fundamental relation ${\mathrm{\Gamma }}^{\ast }$ on an $(m,n)$-hyperring $R$such that $R/{\mathrm{\Gamma }}^{\ast }$ is the smallest $(m,n)$-ring, and then somerelated properties are investigated.