A STUDY ON PSEUDO INTEGRAL TERNARY Γ-SEMIGROUPS

In this paper, the terms; kernel of a ternary Γ-semigroup, pseudo intergral ternary Γ-semigroup and Rees quotient ternary Γ-semigroup are introduced. It is proved that (1) every pseudo symmetric ternary Γ-semigroup with nonempty kernel is a pseudo integral ternary Γ-semigroup. It is also proved that a ternary Γ-ideal A of a ternary Γ-semigroup T is pseudo symmetric iff Rees quotient ternary Γ-semigroup T/A is a pseudo integral ternary Γ-semigroup. It is proved that every minimal prime ternary Γ-ideal of a pseudo integral ternary Γ-semigroup is a completely prime ternary Γ-ideal. If T is a pseudo integral ternary Γ-semigroup then it is proved that T is strongly Archimedean, T is Archimedean, T has no proper completely prime Γ-ideals, T has no proper completely semiprime ternary Γ-ideals, T has no proper prime ternary Γ-ideals, T has no proper semiprime ternary Γ-ideals, every element in T is a K-potent element, are equivalent. It is proved that if S is a maximal ternary Γ-subsemigroup of a pseudo integral ternary Γ-semigroup T such that S ∩ K =∅ then T\S is a minimal prime ternary Γ-ideal in T.