摘要
通过偏序半群的商半拟序、商半拟链和正则同余,研究了偏序半群的商序同态,给出了偏序半群的商序同态基本定理。同时,讨论了偏序半群的商半拟序与商序同态之间的关系,给出了由偏序半群S到T的商序同态φ构造S的商半拟序ρ_φ的方法以及S的一个商半拟序ρ?ρ_φ的充分必要条件,并得到了一些重要结论。
By quotient semi-pseudo order,quotient semi-pseudo chain and regular congruence of partially ordered semigroups,the quotient ordered homomorphisms of partially ordered semigroups are studied,and the fundamental theorems on quotient ordered homomorphisms are given.At the same time,relationships between quotient semi-pseudoorder and quotient ordered homomorphisms of par-tially ordered semigroups are discussed,the construction method on quotient semi-pseudo order of S by quotient ordered homomorphisms from partially ordered semigroups S to T and the sufficient and the necessary conditions on a quotient semi-pseudo orderρ⊆ρφof S are given,and some important conclu-sions are obtained.
作者
邵海琴
梁茂林
董芳芳
李长涛
SHAO Haiqin;LIANG Maoin;DONG Fangfang;LI Changtao(School of Mathematical and Statistical Sciences,Tianshui Normal University,Tianshui 741001,Gansu,China;School of Mathematical and Statistical Sciences,Xianyang Normal University,Xianyang 712000,Shaanxi,China)
出处
《咸阳师范学院学报》
2024年第4期6-9,共4页
Journal of Xianyang Normal University
基金
国家自然科学基金项目(12361081)
甘肃省教育厅创新基金项目(2022B-158)
陕西省自然科学基础研究计划项目(2023JCYB082)。
关键词
偏序半群
商半拟序
商半拟链
正则同余
商序同态
partially ordered semigroups
quotient semi-pseudoorder
quotient semi-pseudochain
regular congruence
quotient ordered homomorphisms