Abstract

ABUNDANT SEMIGROUPS OF VARIANT FINITE FULL TRANSFORMATION

M. Balarabe, G. U. Garba & A. T. Imam

---

Abstract Given a fix element a of a semigroup S, we can always obtain a new semigroup whose underlying set is S and binary operation defined by x*_a y=xay for all x,y ? S, where the concatenation denote the original binary operation on S. The new semigroup denoted by S^ais referred to variant of S by a. In this article, we prove that every variant of semigroup S by an idempotent is embeddable in a variant of full transformations semigroups. We characterized starred Green’s relations L^* and R^* in the variant of finite full transformation semigroup and showed that the semigroup is abundant. Keywords: Variant full transformation, Green’s relations, Starred Green’s relations, abundant semigroup.

PDF