A study on regularity and reduction for n-ary semihypergroups

Abstract

In this paper, we construct new [Formula: see text]-ary semihypergroups induced by subsets of the base sets of [Formula: see text]-ary semigroups. Then, we investigate some algebraic connections between the [Formula: see text]-ary semihypergroups and [Formula: see text]-ary semigroups via the concept of regularity on [Formula: see text]-ary semihypergroups. We also discover some significant conditions on [Formula: see text]-ary semihypergroups which can be reduced to semihypergroups.