**InternationaleJournals**

**IDEALS IN TERNARY SEMIGROUPS**

**Y.
Sarala ^{1}, A.Anjaneyulu^{2}, D.Madhusudhana Rao^{3}**

**ABSTRACT**

In this paper
the terms ideal, trivial ideal, proper ideal, maximal ideal are introduced. It is proved that the union and intersection
of any family of ideals of ternary semigroup T is an ideal of T. It is also
proved that union of all proper ideals of ternary semigroup T is the unique
maximal ideal of T. The terms ideal of
ternary semigroup T generated by A, principal ideal generated by an element are
introduced. It is proved that the ideal
of a ternary semigroup T generated by a non-empty subset A is the intersection
of all ideals of T containing A. It is
also proved that T is a ternary semigroup and *a*

J(*a*) = *a**a*TT*a**a*T*a*TT . The
terms, simple ternary semigroup, globally idempotent ideal are introduced. In
any ternary semigroup T, principal ideals of T form a chain and ideals of T
form a chain are equivalent. It is
proved that a ternary semigroup T is simple ternary semigroup if and only if TTaTT
= T for all *a*

**Mathematics Subject Classification:** 20M12, 20N10, 60F03, 20N99

**Key words**: Ideal, trivial
ideal, proper ideal, chain, ideal of ternary semigroup T generated by A,
principal ideal generated by *a*, simple ternary semigroup T.

** **

**International
eJournal of Mathematics and Engineering**

**Volume 4,
Issue ****1,** **Pages: ** 1950 - 1968