• U-Γ-SEMIGROUPS AND V- Γ-SEMIGROUPS

S. SAVITHRI*, A. GANGADHARA RAO, L. ACHALA, J. M. PRADEEP

Abstract


In this paper, the terms, Maximal Γ-ideal, primary Γ-semigroup, prime Γ-ideal, simple Γ-semigroup, U- Γ-semigroup and V- Γ-semigroup  are introduced. It is proved that Γ-semigroup S is a U- Γ-semigroup if either S has a left (right ) identity or S is generated by a Γ-idempotent.  Also it is proved that a Γ-semigroup S is a U- Γ-semigroup if and only if every proper Γ-ideal is contained in a proper prime Γ-ideal.  Also it is proved that if A is a proper Γ-ideal in the finite dimensional U- Γ-semigroup S, then A is contained in maximal Γ-ideal and also it is proved that if S is a globally idempotent Γ-semigroup with maximal Γ-ideals, then either S is aV- Γ-semigroup or S has a unique maximal Γ-ideal which is prime.


Keywords


Γ-semigroup, Maximal Γ-ideal, primary Γ-semigroup, commutative Γ-semigroup, left (right) identity, identity, Zero element, Prime Γ-ideal, simple Γ-semigroup, U- Γ-semigroup and V- Γ-semigroup.

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