| 全子半群构成链的富足半群 |
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| 引用本文： | 郭俊颖,郭小江,刘珊珊. 全子半群构成链的富足半群[J]. 数学学报, 2017, 60(3): 439-450 |
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| 作者姓名： | 郭俊颖 郭小江 刘珊珊 |
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| 作者单位： | 1. 江西师范大学科技学院 南昌 330027;2. 江西师范大学数学与信息科学学院 南昌 330022 |
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| 基金项目： | 国家自然科学基金（11361027，11661042）；江西省自然科学基金（20161BAB201018）；江西省教育厅科研资助项目（GJJ14251）及省研究生创新基金资助项目（YC2014-S160） |
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| 摘 要： | 全子半群定义为含有所有幂等元的子半群.半群称为▽_(fs)-半群,如果它的所有全子半群关于集合包含关系构成一个链.本文研究富足▽_(fs)-半群,得到这类半群的若干特征,特别地,建立了完全0-单▽_(fs)-半群和满足正则性条件的本原富足▽_(fs)-半群的结构.
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| 关 键 词： | 富足半群 全子半群 链 正则性条件 |
Abundant Semigroups Whose Full Subsemigroups form a Chain |
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| Jun Ying GUO,Xiao Jiang GUO,Shan Shan LIU. Abundant Semigroups Whose Full Subsemigroups form a Chain[J]. Acta Mathematica Sinica, 2017, 60(3): 439-450 |
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| Authors: | Jun Ying GUO Xiao Jiang GUO Shan Shan LIU |
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| Affiliation: | 1. College of Science and Technology, Jiangxi Normal University, Nanchang 330027, P. R. China;2. College of Mathematics and Information Science, Jiangxi Normal University, Nanchang 330022, P. R. China |
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| Abstract: | Full subsemigroups are defined as subsemigroups containing all idempotents. A semigroup is said to be a ▽fs-semigroup if its full subsemigroups form a chain under inclusion. The aim of this paper is to investigate abundant ▽fs-semigroups. Some characterizations of such semigroups are obtained. In particular, the structures of completely 0-simple ▽fs-semigroups and primitive abundant ▽fs-semigroups satisfying the regularity condition are established. |
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| Keywords: | abundant semigroup full subsemigroup chain the regularity condition |
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