Some Studies On Q-regular Semigroups

We study Q-regular semigroups in this paper which is divided into four parts.The first part is introduction and preparation knowledge. The concept of Q-regular semigroups and some related results are introduced, and we give some char-acterizations of Q-regular semigroups. In the second part, the characteristic set ofQ-regular semigroups is studied. We give a normal partition of Q, in the same time, weprove that there exists an μNon S(Q) which is the greatest strong Q-congruence suchthat ctrμN=πNfor any normal partition N of Q. In the third part, we introduce theconcept of all Q-full and Q-self-conjugate subsemigroups of Q-regular semigroups, andcharacterize the group congruence on Q-regular semigroups. Several equivalent expres-sions for any group congruence on Q-regular semigroups are given. In the forth part, aconstruction of Q-subdirect products of Q-regular semigroups is given, and E-unitarycovers of Q-regular semigroups are discussed, in particular for those whose maximumgroup homomorphic image is a given group.