摘要
证明了P 正则半群S(P)的强P 同余格与S(P)上强P 同余对所成的格同构;在S(P)的强P 同余格上定义了θ 关系,刻画了具有θ 关系的两个强P 同余的联和交的强P 核正规系,并证明了S(P)的强P 同余格与强P 核正规系格同构.所得结论是当前一些文献中已有结果的深化.
Let S(P) be a PBX-regular semigroup. In this paper, it is proved that the strong P-congruence lattice and strong P-congruence-pair lattice of S(P) are isomorphic. Moreover the θ-relation is defined by so-called c-trace on the strong P-congruence lattice Λ_P(S). Further, a characterization of strong P-kernel normal systems is given for the join and meet of two strong P-congruences which are in the same θ-class. Finally, it is also proved that the strong P-congruence lattice and the lattice of strong P-kernel normal systems on S(P) are isomorphic. The results obtained here deepened some relative results in recent literature.
出处
《四川师范大学学报（自然科学版）》
CAS
CSCD
2004年第5期471-475,共5页
Journal of Sichuan Normal University（Natural Science）
基金
四川省教育厅重点科研基金资助项目
关键词
P-正则半群
强P-同余
格同构
p-关系
强p-核正规系
P-regular semigroup
Strong P-congruence
Lattice isomorphism
θ-relation
Strong P-kernel normal system
