偏序半群的偏序和商序满同态的若干重要性质  

Some Important Properties Partially Ordered and Quotient Ordered Surjective Homomorphisms of Partially Ordered Semigroups

作　　者：邵海琴[1] SHAO Haiqin(School of Mathematics and Statistics Institute, Tianshui Normal University, Tianshui 741001, Gansu, Chin)

机构地区：[1]天水师范学院数学与统计学院,甘肃天水741001

出　　处：《咸阳师范学院学报》2018年第2期39-43,共5页Journal of Xianyang Normal University

基　　金：甘肃省教育厅科学研究基金项目(2015A-129)

摘　　要：通过偏序半群的同余、正则同余和反强正则同余,对偏序半群的偏序满同态与商序满同态进行了刻画,得到偏序半群的偏序满同态是保同余关系,保正则同余关系的和偏序半群的商序满同态是保反强正则同余关系。讨论了偏序半群的偏序满同态在偏序半群的正则同余的同余类和包含正则同余的最小拟序上的作用,以及偏序半群的商序满同态在偏序半群的包含反强正则同余的最小拟序上的作用,得到了一些重要结论。In this paper, through a discussion of congruence, regular congruence and inverse strong- ly regular congruence of partially ordered semigroups, partially ordered surjective homomorphisms and quotient ordered surjective homomorphisms of partially ordered semigroups are depicted. Obtained are some important properties that partially ordered surjective homomorphisms of partially ordered semi- groups are congruence relation-preserving, regular congruence relation-preserving, and quotient or- dered surjective homomorphisms of partially ordered semigroups are inverse strongly regular congru- ence-preserving. Simultaneously, considered is the effect of partially ordered surjective homomor- phisms of partially ordered semigroups on congruence class of regular congruence and minimal pseu- doorder including regular congruence, with effect of quotient ordered surjective homomorphisms of par- tially ordered semigroups on minimal pseudoorder including inverse strongly regular congruence also considered, and with some important conclusions obtained.

关 键 词：偏序半群 同余 正则同余 反强正则同余 偏序满同态 商序满同态 

分 类 号：O152.7[理学—数学]