关于Q-正则半群的若干的研究.doc

uQ-  K?+ á ?  eZ??  ??? Q-  K?+.  ?  ?·où. 1?ù′úó?y ·￡, 0 Q- K?+ Vg9?(J, ‰? Q- K?+ eZ5?. 1 ù?? Q- K?+ A 8, ‰?A 8 5y? Vg. ó?y2uA 8 ?? 5y? N, ·3 S(Q) | ctrμN = πN ·?r Q-ó{ μN . 1nùú\ Q- K?+ Q-÷ Q-g Yf?+ V g, ?|^dVg‰? Q- K?+t +ó{ ·x9ùeZ d￡?. 1 où?? Q- K?+ Q-g?è, ‰? Q- K?+ Q-g?è E, ?? ? Q- K?+ E-jCX, AO′ù·?+ó –·‰?+ ?/.  …c:  Q-  K?+; A  8; +ó{; Q-g?è; E-jCX.  i SOME STUDIES ON Q-REGULAR SEMIGROUPS ABSTRACT We study Q-regular semigroups in this paper which is divided into four parts. The ?rst 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 of Q-regular semigroups is studied. We give a normal partition of Q, in the same time, we prove that there exists an μN on S(Q) which is the greatest strong Q-congruence such that ctrμN = πN for any normal partition N of Q. In the third part, we introduce the concept of all Q-full and Q-self-conjugate subsemigroups of Q-regular semigroups, and characterize 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, a construction of Q-subdirect products of Q-regular semigroups is given, and E-unitary covers of Q-regular semigroups are discussed, in particular for those whose maximum group homomorphic image is a given group.  Key words:  Q-regular semigroup; characteristic set; group congruence; Q-subdirect product; E-unitary cover. ii 8  1  1?ù úó?y  ·￡ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1 ù A 8 5y?. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .7 1nù Q- 1où Q- K?+t K?+ +ó{ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10 Q-g?è . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .