Ternary Semigroups

1Y. Sarala, 2A.Anjaneyulu and 3D.Madhusudhana Rao

1Dept. of Mathematics, Nagarjuna University, Guntur, A.P. India. Email:

2Dept. of Mathematics, V S R & N V R College, Tenali, A.P. India. Email:

3Dept. of Mathematics, V S R & N V R College, Tenali, A.P. India. Email:


In this paper the terms; quasi commutative ternary semigroups, normal ternary semigroups, pseudo commutative ternary semigroups are introduced. Unital element and zero element in a ternary semigroups are introduced. It is proved that every commutative ternary semigroup is a normal ternary semigroup and a Pseudo commutative ternary semigroup. It is proved that a ternary semigroup T has atmost one identity element and atmost one zero element. If A be a non-empty subset of a  ternary semigroup T then it is proved that <A> = the intersection of all ternary subsemigroup of T containing A. The terms idempotent element , regular element, completely regular element, intra regular element, semisimple elemenet are introduced. It is proved that a be a left regular (or) lateral regular (or) right regular element of a  ternary semigroup T then a is semisimple lelment of T. The terms arthimedean, strongly arthemedean ternary semigroups are introduced. Finally it is proved that every strongly a  ternary semigroup T is an arthemedean ternary semigroup.

Mathematics Subject Classification : 20M12 , 20N10, 60F05,20N99

Key words : Quasi commutative, normal, pseudo commutative, ternary subsemigroup of  T generated by A, semisimple elements, regular ternary semigroup, completely regular ternary semigroup, ideal, principal ideal, idempotent, archimedean semigroup.




International eJournal of Mathematical Sciences, Technology and Humanities

Volume 2, Issue 5, Pages:  848 - 859