A NEW CONSTRUCTION FOR REGULAR SEMIGROUPS WITH QUASI-IDEAL ORTHODOX TRANSVERSALS
Xiangjun Kong, Xianzhong Zhao · Journal of the Australian Mathematical Society · 2009
Abstract In any regular semigroup with an orthodox transversal, we define two sets R and L using Green’s relations and give necessary and sufficient conditions for them to be subsemigroups. By using R and L, some equivalent conditions for an orthodox transversal to be a quasi-ideal are obtained. Finally, we give a structure theorem for regular semigroups with quasi-ideal orthodox transversals by two orthodox semigroups R and L.