Indian Journal of Science and Technology

Abstract

Objective/Background: In this paper, the concept of commutative ternary right almost semigroups is introduced. The properties of ternary right almost semigroups and commutative ternary right almost semigroups are also discussed. Finally, regular only and the regularity are also explored in ternary right almost semigroups. Methods: Properties of ternary right almost semigroup have been employed to carry out this research work to obtain all the characterizations of commutative ternary right almost semigroups, regular and normal corresponding to that ternary semigroup. Findings: We call an algebraic structure is a ternary semigroup if is a Semigroup, is a ternary semigroup under ternary multiplication. Let be a groupoid. Then it is a right almost semigroup ( -semigroup), if we have for all (i) -semigroup - -cyclic if for all (ii) -semigroup - -cyclic if for all In this ternary structure we try to study commutative ternary semigroups concept and obtain their properties. Novelty: In this study, we define the notion of some properties of commutative ternary right almost semigroups, regular and normal. We also find some of their interesting results. AMS Subject Classification code: 20M12, 20N10

Keywords: Ternary semigroups, Ternary right almost semigroup, Commutative ternary right almost semigroups, Quasi- commutative ternary right almost semigroups, Regular ternary right semigroups and Normal ternary right almost semigroups