Characterization of Left Almost Semigroups by Their Ideals

LA-semigroups have been studied in many articles in details. In this paper we have proved some results on quasi-ideals and bi-ideals in an LA-semigroup. Further we have characterized an intra-regular LA-semigroup by the properties of its ideals. It has been proved that in an intra-regular LA-semigroup left, right, two-sided, interior, bi-, generalized bi- and quasi-ideals coincide. Further, we prove that the set of all ideals of an intra-regular LA-semigroup forms a semilattice structure.