| 偏序半群的C-左理想 |
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| 引用本文： | 谢祥云,郭小江.偏序半群的C-左理想[J].数学学报,1997,40(6):861-866. |
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| 作者姓名： | 谢祥云 郭小江 |
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| 作者单位： | [1]五邑大学数理系 [2]兰州大学数学系 |
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| 基金项目： | 广东省自然科学基金，国家教委博士点专项基金 |
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| 摘 要： | 本文引入了偏序半群中Ｃ 左理想的概念，讨论了Ｃ 左理想的一些基本性质，定义了左基的概念并利用它给出了最大Ｃ 左理想存在的必要和充分条件．作为应用，本文还讨论了每个真左理想均为Ｃ 左理想和无Ｃ 左理想这两类半群的结构特征．本文的结果在一般半群中也成立
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| 关 键 词： | C－左理想，左基，极大L－类，最大C－左理想 |
| 收稿时间： | 1995-11-14 |
| 修稿时间： | 1996-10-3 |
On C-letft Ideals in Ordered Semigroups |
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| Institution: | Xie Xiangyun(Department of Mathematics and Physics,Wuyi University, Jiangmen 529020; China, Fax: 0750-3354323, E-mail:xyxie@letterbox.wyu.edu.cn; Guo Xiaojiang( Department of Mathematics, LanzhouUniversity, Lanzhou 730000, China)) |
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| Abstract: | In this paper we introduce and study the C-left ideals of ordered semigroups. We discuss some elementary properties of C-left ideals, and give out the sufficient and necessary conditions of the existence of the greatest C-left ideal of an ordered semigroup by the concept of left bases of an ordered semigroup which is introduced in this paper. As an application, we characterize two classes ordered semigroups: C-left simple ordered semigroups and ordered semigroups which every proper left ideal is C-left ideal. The corresponding results on semigroups——without order——are obtained as an application of the results of this paper in the way indicated in . |
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| Keywords: | C-left ideal Left base Maximal L-class Greatest C-left ideal |
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