| 序半群的理想扩张 |
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| 引用本文： | 谢祥云. 序半群的理想扩张[J]. 五邑大学学报(自然科学版), 2003, 17(1): 11-17 |
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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项目(No. 6007514 )，广东省“千百十”工程人才基金资助项目(No.Q校02050) |
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| 摘 要： | 介绍序半群的理想扩张和n-素理想，研究它们之间的关系。设计S是交换半群。如果S有单位元，则S的n-素理想与（n-1)-素理想一致（n≥3)。如果I为S的n-素理想（n≥3)，则I是S中包含它的所有（n-1)-素理想的交。作为结果，如果S是半格则S的每个n-素理想（n≥3)是S中包含它的（n-1)-素理想之交。
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| 关 键 词： | 序半群 素理想 理想扩张 |
| 文章编号： | 1006-7302(2003)01-0011-07 |
| 修稿时间： | 2001-08-27 |
On the Ideal Extensions in Ordered Semigroups |
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| XIE Xiang-yun. On the Ideal Extensions in Ordered Semigroups[J]. Journal of Wuyi University(Natural Science Edition), 2003, 17(1): 11-17 |
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| Authors: | XIE Xiang-yun |
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| Abstract: | The aim of this paper is to introduce the extensions of ideals and -nprime ideals in ordered semigroups and to study the relation ship between them. Let S be a commutative ordered semigroup. If S has an identity element, then the -nprime ideal and the )1(-n-prime ideals coincide )3(n. If I is a -nprime ideal of S)3(n, then I is the intersection of the )1(-n-prime ideals of S containing it. As a consequence, if S is a semilattice, the every -nprime ideal of, 3n, is the intersection of the )1(-n-prime ideals of S containing it. |
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| Keywords: | ordered semigroup prime ideal extension of ideal |
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