P-正则半群的强P-同余格

THE LATTICE OF STRONG P-CONGRUENCES OF A P-REGULAR SEMIGROUP

证明映射 ctr:ρ|→ ctrρ为格∧P (S)到格Σ(P)上的完全格同态 ,且由 ctr诱导的∧P(S)上的同余θ的每一个同余类为∧P(S)的完全模子格 .给出同余θ的若干等价刻划 .

In this paper, it is shown that the mapping ρ|ctr ρ is a complete homomorphism of the strong P congruence lattice of S(P) onto the lattice of normal equivalences on P , and that the congruence θ induced by it has all its classes complete modular lattices. Some characterizations of θ are given.