On Certain Categories of Non-Associative Cyclic Hypergroup

Abstract

Numerous generalizations of the rudimentary concept of hypergroups have been explored since its introduction by Marty. In this paper, we consider a notable category of non-associative cyclic hyperstructures named as single power cyclic LA-hypergroups which are a conception of cyclic hypergroups and LA-semigroups. We enumerate single power cyclic LA-hypergroups of order two (and three) and period two. Additionally, we investigate some features of these single power cyclic LA-hypergroups. We also study various properties of cyclic LA-hypergroups and examine the differences between cyclic groups and cyclic LA-hypergroups.