a1 School of Mathematical Sciences, Qufu Normal University, Qufu, Shandong 273165, People’s Republic of China
a2 Department of Mathematics, Northwest University, Xi’an, Shaanxi 710069, People’s Republic of China
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.
(Received November 25 2006)
(Accepted December 12 2007)
2000 Mathematics subject classification
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