A study on regularity and reduction for n-ary semihypergroups

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.