| 偏序带的偏序扩张 |
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| 引用本文： | 谢祥云.偏序带的偏序扩张[J].苏州科技学院学报(自然科学版),2004,21(1):17-21. |
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| 作者姓名： | 谢祥云 |
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| 作者单位： | 五邑大学,数学物理系,广东,江门,529020 |
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| 基金项目： | 国家自然科学基金资助011471，广东省自然科学基金(000864)，广东省教育厅基金项目Z03070，广东省教育厅“千百十工程”优秀人才基金资助项目(No.Q校02050)资助。 |
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| 摘 要： | 给出将偏序幺半格和偏序带S·≤上的偏序≤扩张为全序幺半格和带S·≤的充要条件。作为应用,得到文献1结论:设S·是幺带,存在S上的平凡序的全序扩张≤使得S·≤是全序幺带当且仅当S的每个D类至多有两个元素。
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| 关 键 词： | 偏序半群 偏序扩张 偏序半格 偏序带 可消偏序 |
| 文章编号： | 1672-0687(2004)01-0017-05 |
| 修稿时间： | 2003年11月27 |
On Extensions of Partial Orders of Partially Ordered Bands |
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| XIE Xiang-yun.On Extensions of Partial Orders of Partially Ordered Bands[J].Journal of University of Science and Technology of Suzhou,2004,21(1):17-21. |
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| Authors: | XIE Xiang-yun |
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| Abstract: | In this paper, the sufficient and necessary conditions for extending partial orders of partially ordered semi-lattices and partially ordered bands to linearly orderes are given. By way of application, the result is obtained that there exists a total order on a band with identity so that it is a totally ordered band only if every D class has at most 2 elements . |
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| Keywords: | Partially ordered semi-group: partially ordered extension: partially ordered semi-lattice: partially ordered band: cancellable partial order |
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