Pseudo Integral Γ-Semigroup
D. Madhusudhana Rao1, A. Anjaneyulu2, A. Gangadhara Rao3
1Department of Mathematics, VSR & NVR College, Tenali, A.P. India. Email: firstname.lastname@example.org
2Department of Mathematics, VSR & NVR College, Tenali, A.P. India. Email: email@example.com
3Dept. of Mathematics, VSR & NVR College, Tenali, A.P. India. Email: firstname.lastname@example.org
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