On Left and Right A-Ideals of a Γ-Semigroup

Khwancheewa Wattanatripop, Thawhat Changphas

Abstract

In this paper, we define the concepts of left A-ideals and right Aideals of a Γ-semigroup. The main result is a characterization of a Γ-semigroup
contains no proper left (respectively, right) A-ideals. Indeed, it is proved that a
Γ-semigroup S contains no proper left (respectively, right) A-ideals if and only if
(1) S is a left (respectively, right) zero Γ-semigroup; or (2) (S, γ) is a group for
all γ ∈ Γ and the cardinality |S| = 2. It is observed that the result obtained by
Grosek and Satko [1] become then a special case.