完全正则子半群格是半模格的完全正则半群

兰州理工大学学报 ›› 2020, Vol. 46 ›› Issue (2): 155-157.

完全正则子半群格是半模格的完全正则半群

田振际, 胡运华, 陶禹桦

兰州理工大学理学院, 甘肃兰州 730050

收稿日期:2018-03-01 出版日期:2020-04-28 发布日期:2020-06-23
作者简介:田振际(1964-),男,甘肃会宁人,博士,教授.
基金资助:
国家自然科学基金(11261030)

Completely regular semigroups whose lattice of completely regular subsemigroups is semimodular

TIAN Zhen-ji, HU Yun-hua, TAO Yu-hua

School of Science, Lanzhou Univ. of Tech. , Lanzhou 730050, China

Received:2018-03-01 Online:2020-04-28 Published:2020-06-23

摘要/Abstract

摘要： 得到了完全正则半群S的子系统格是半模格的充分必要条件,即S的子系统格是半模格当且仅当S是一些UM-群或者极大子群为UM-群的左群或右群的序和.

关键词: 完全正则半群, 完全正则子半群格, 半模格

Abstract: Otain the necessary and sufficient condition that the subsystem lattice of a completely regular semigroup S is a semimodular lattice, that is, the subsystem lattice of S is a semimodular lattice if and only if S is the order sum of some UM-groups or left [right] groups whose maximal subgroups are UM-groups.

Key words: completely regular semigroups, completely regular subsemigroups lattice, semimodular lattice

中图分类号:

O153.1

田振际, 胡运华, 陶禹桦. 完全正则子半群格是半模格的完全正则半群[J]. 兰州理工大学学报, 2020, 46(2): 155-157.

TIAN Zhen-ji, HU Yun-hua, TAO Yu-hua. Completely regular semigroups whose lattice of completely regular subsemigroups is semimodular[J]. Journal of Lanzhou University of Technology, 2020, 46(2): 155-157.