Regularities in ordered n-ary semihypergroups

Abstract

This paper deals with a class of hyperstructures called ordered n-ary semihypergroups which are studied by means of j-hyperideals for all positive integers 1 ≤ j ≤ n and n ≥ 3. We first introduce the notion of (softly) left regularity, (softly) right regularity, (softly) intra-regularity, complete regularity, generalized regularity of ordered n-ary semihypergroups and investigate their related properties. Several characterizations of them in terms of j-hyperideals are provided. Finally, the relationships between various classes of regularities in ordered n-ary semihypergroups are also established.