具有Q-正则*-断面的正则半群上的*-同余格

文中给出了一个具有正则*-断面正则半群的例子,该半群同时存在非平凡*-同余和非平凡的非*-同余;证明了正则*-断面上的每个*-同余都能扩张成整个半群上的*-同余;刻划了*-同余和*-同余格;定义了*-同余格上的两个完全同余T*FS和T*S*;研究了*-同余格上的完全同余T*S*, T*, T*l, Tr, U*和V*, 给出了这些同余的类中的极值同余(除U*, V*外).

On *-Congruence Lattice of a Regular Semigroup with a Q-Regular *-transversal

Let S be a regular semigroup. A subsemigroup S* of S is called a regular *-transversal if there exists a unary operation * on S such that (1) x*∈S*∩V(x) for any x∈S; (2) (x*)*=x for any x∈S*; (3) (x*y)*=y*x** and (xy*)*=y**x* for any x,y∈S, where x**=(x*)*. In this paper, we give an example of such a semigroup on which there is a non-trivial *-congruence and prove that if S* is a quasi-ideal regular *-transversal of S then every *-congruence on S* can be extended to a *-congruence on S. We describe that the characterizations of *-congruence on S and *-congruence lattice of S. We define two complete congruences T*FS*, and T*S* on Con*(S) and discuss the complete congruences T*S*, T*, T*l, T*rU* and V*, on the *-congruence lattice Con*(S) of S and describe the extremal values in the classes of these congruences except for U* and V*.