具有Q-正则*-断面的正则半群上的*-同余格(英文)

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

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 )

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* F S*, 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*.