MATEMATIČKI VESNIK
МАТЕМАТИЧКИ ВЕСНИК



MATEMATIČKI VESNIK
Constructions of $(m,n)$-hyperrings
S. Mirvakili and B. Davvaz

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.

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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