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数学进展 - 2020, Vol. 49(4): 429-442
研究论文
半模弱Brandt半群
Semimodular Weak Brandt Semigroups

郭俊颖1, 郭小江2, 肖芬芬2
GUO Junying1,*, GUO Xiaojiang2, XIAO Fenfen2

1.江西师范大学科技学院, 南昌, 江西, 330022;
2.江西师范大学数学与信息科学学院, 南昌, 江西, 330022
1. College of Science and Technology, Jiangxi Normal University, Nanchang, Jiangxi, 330022, P. R. China;
2. College of Mathematics and Information Science, Jiangxi Normal University, Nanchang, Jiangxi, 330022, P. R. China

收稿日期: 2019-06-15
出版日期: 2020-08-11
2020, Vol. 49(4): 429-442
DOI: 10.11845/sxjz.2019068b


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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.
关键词 (本原半单) ample半群全子半群(分配,模,半模)格    
Abstract: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)
Key words(primitively semisimple) ample semigroup    full subsemigroup    (distributive,modula,semimodular) lattice
PACS:  O152.7  
通讯作者: E-mail: * xjguo@jxnu.edu.cn   
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[1] 邵勇*,任苗苗. 纯正半群上的一类偏序关系[J]. 数学进展, 2013, 42(4): 458-464.
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