一类图逆半群的同余格的性质  

Properties of the Congruence Lattice for a Class of Graph-Inverse Semigroups

作　　者：罗天红 罗永乐 王正攀[1] LUO Tian-hong;LUO Yong-le;WANG Zheng-pan(School of Mathematics and Statistics,Southwest University,Chongqing 400715,China)

机构地区：[1]西南大学数学与统计学院,重庆400715

出　　处：《西南大学学报（自然科学版）》2021年第4期73-78,共6页Journal of Southwest University(Natural Science Edition)

基　　金：国家自然科学基金项目(12071375).

摘　　要：给定有向图,其上的图逆半群的同余格是上半模格,但通常不是下半模格.借助同余三元组的语言,利用具有覆盖关系的同余三元组所表现出的性质,通过分类讨论,证明了顶点指数最多为1的连通图上的图逆半群的同余格是下半模格.The congruence lattice of the graph-inverse semigroup on a given directed graph is upper semimodular,but not necessarily lower semimodular.In terms of congruence triples,we prove that the congruence lattices of graph-inverse semigroups defined on graphs,each of whose vertices has an index of at most 1,are lower semimodular by using the properties of covering between congruence triples and classification discussion.

关 键 词：图逆半群 同余 同余格 上半模格 下半模格 

分 类 号：O152.7[理学—数学]