PSEUDO INTEGRAL -SEMIGROUP
D. Madhusudhana Rao, A. S. R. Anjaneyulu, A. Gangadhara Rao · 2011
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 Γsemigroup (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 Γsemigroup 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 Kpotent element are equivalent. It is proved that if T is a maximal Γ-subsemigroup of a pseudo integral Γ-semigroup S such that