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Pseudo Integral  Γ-Semigroup

D. Madhusudhana Rao1, A. Anjaneyulu2, A. Gangadhara Rao3

1Department of Mathematics, VSR & NVR College, Tenali, A.P. India. Email: dmrmaths@gmail.com

2Department of Mathematics, VSR & NVR College, Tenali, A.P. India. Email: anjaneyulu.addala@gmail.com

3Dept. 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.

KEY WORDS:  Pseudo symmetric Γ-ideal, semipseudo symmetric Γ-ideal, Kernel, Rees quotient ݚª-semigroup, prime Γ-ideal, semiprime Γ-ideal, completely prime Γ-ideal, completely semiprime Γ-ideal, semisimple element, A-potent element, A-potent Γ-ideal, A-divisor, pseudo integral ݚª-semigroup.

 

 

 


International eJournal of Mathematical Sciences, Technology and Humanities

Volume 1, Issue 2, Pages:  118 - 124