摘要
全子半群定义为包含所有幂等元的子半群.众所周知,一个半群所有全子半群关于集合的包含关系构成格.一个ample半群称为分配的(模的;半模的),如果其全子半群格为分配格(模格;半模格).本文得到了弱Brandt半群成为半模(模;分配)ample半群的充分必要条件.作为应用,确定了本原半单ample半群何时为模(分配)ample半群.
Full subsemigroups are defined as subsemigroups containing all idempotents.It is well known that all full subsemigroups of a semigroup form a lattice under the inclusion.An ample semigroup is said to be distributive(modular;semimodular)if its lattice of full subsemigroups is distributive(modular;semimodular).In this paper a sufficient and necessary condition is obtained for a weak Brandt semigroup to be semimodular(resp.modular;distributive).As an application,it is determined when a primitively semisimple ample semigroup is modular(resp.,distributive).
作者
郭俊颖
郭小江
肖芬芬
GUO Junying;GUO Xiaojiang;XIAO Fenfen(College of Science and Technology,Jiangxi Normal University,Nanchang,Jiangxi,330022,P.R.China;College of Mathematics and Information Science,Jiangxi Normal University,Nanchang,Jiangxi,330022,P.R.China)
出处
《数学进展》
CSCD
北大核心
2020年第4期429-442,共14页
Advances in Mathematics（China）
基金
NSFC(Nos.11761034,11361027,11661042)
Natural Science Foundation of Jiangxi Province(No.20161BAB201018)。
关键词
(本原半单)ample半群
全子半群
(分配
模
半模)格
(primitively semisimple)ample semigroup
full subsemigroup
(distributive
modular
semimodular)lattice
