**InternationaleJournals**

**Pseudo
Integral ****Γ****-Semigroup
**

**D.
Madhusudhana Rao ^{1}, A. Anjaneyulu^{2}, A. Gangadhara Rao**

^{1}Department
of Mathematics, VSR & NVR College, Tenali, A.P.
India. Email: __dmrmaths@gmail.com__

^{2}Department
of Mathematics, VSR & NVR College, Tenali, A.P.
India. Email: __anjaneyulu.addala@gmail.com__

^{3}Dept.
of Mathematics, VSR & NVR College, Tenali, A.P.
India. Email: __raoag1967@gmail.com__

**ABSTRACT**

In this paper, the term,
‘pseudo intergral Γ-semigroup’
is introduced. It is proved that

(1) every pseudo symmetric Γ-semigroup
with nonempty kernel is a pseudo integral Γ-semigroup
(2) If S is a Γ-semigroup
with empty kernel such that S has no nontrivial K-divisor elements then S is a
pseudo integral Γ-semigroup. It is also proved that a Γ-ideal A of a Γ-semigroup S is pseudo
symmetric iff S\A is a pseudo integral Γ-semigroup. If S is a pseudo integral Γ-semigroup then it is proved
that S is strongly archimedean, S is archimedean, S has no proper completely
prime Γ-ideals, S has no proper completely
semiprime Γ-
ideals, S has no proper prime Γ-ideals,
S has no proper semiprime Γ-ideals,
every element in S is a K-potent element are equivalent. It is proved that if T is a maximal Γ-subsemigroup of a pseudo
integral Γ-semigroup
S such that then S\T is a minimal
prime Γ-ideal in S.

**Mathematical subject classification (2010)** :
20M07; 20M11; 20M12.

**International
eJournal of Mathematical Sciences, Technology and Humanities**

**Volume** 1,
**Issue** 2, **Pages**: 118 - 124