半模弱Brandt半群  

Semimodular Weak Brandt Semigroups

作　　者：郭俊颖[1] 郭小江[2] 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)

机构地区：[1]江西师范大学科技学院,江西南昌330022 [2]江西师范大学数学与信息科学学院,江西南昌330022

出　　处：《数学进展》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)。

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).

关 键 词：(本原半单)ample半群 全子半群 (分配 模 半模)格 

分 类 号：O152.7[理学—数学]