The P-regular Semigroups With The P-orthodox Transversal

This thesis mainly studies the P-regular semigroups with the P-orthodox transver-sal, which can be divided into four chapters. The first chapter is introduction, it brieflyintroduces several transversals of the regular semigroups and the results of the thesis.In the second chapter, we introduce the concept of the P-orthodox transversal of theP-regular semigroup. At the same time, not only we study the relationship betweenthe P-orthodox transversal of the P-regular semigroups and the orthodox transversal ofthe P-regular semigroups, but also the relationship between the P-orthodox transversalof the P-regular semigroups and the regular*-transversal of the P-regular semigroups.Some properties of the P-orthodox transversal are studied in the third chapter. Wemainly discuss the relationship between the P-orthodox transversal of the P-regularsemigroups and the sub-semigroups of the P-regular semigroups and the saturation ofD in the P-orthodox transversal of the P-regular semigroups. We also describe theequivalent conditions of quasi-ideal which is P-orthodox transversal of the P-regularsemigroups. With the set R and the relation K, the structure of P-regular semigroupswith the P-orthodox transversal is constructed in the last chapter of this thesis.