Abundant semigroups with weakly simplistic RGQA transversals

As the real common generalisations of both orthodox transversals and adequate in abundant semigroups, concept refined generalised quasi-adequate transversals, briefly, RGQA was introduced by Kong Wang. In this paper, for transversal, necessary sufficient condition sets I ? to be bands is investigated. It demonstrated that are if only transversal weakly simplistic. Moreover, So being simplistic different from a quasi-ideal nor semigroup S satisfying regularity condition. Finally, means band, structure theorem an with established.