| 偏序集上的局部极大理想 |
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| 引用本文： | 姜广浩,王戈平. 偏序集上的局部极大理想[J]. 徐州师范大学学报(自然科学版), 2006, 24(1): 11-14 |
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| 作者姓名： | 姜广浩 王戈平 |
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| 作者单位： | 1. 南京大学,数学系,江苏,南京,210093
2. 徐州师范大学,数学系,江苏,徐州,221116 |
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| 基金项目： | 国家自然科学基金资助项目(10371079) |
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| 摘 要： | 在偏序集上引入并考察了偏序集上的局部极大理想,证明了偏序集上的局部极大理想的存在性定理和偏序集上理想的分解定理,特别地,在满足理想降链条件的偏序集上理想的分解定理.
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| 关 键 词： | 偏序集 局部极大理想 分解 |
| 文章编号： | 1007-6573(2006)01-0011-04 |
| 收稿时间： | 2005-10-11 |
| 修稿时间： | 2005-10-11 |
Locally Maximal Ideals on Posets |
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| JIANG Guang-hao,WANG Ge-ping. Locally Maximal Ideals on Posets[J]. Journal of Xuzhou Normal University(Natural Science Edition), 2006, 24(1): 11-14 |
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| Authors: | JIANG Guang-hao WANG Ge-ping |
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| Affiliation: | 1, Department of Mathematics, Nanjing University, Nanjing, Jiangsu, 210093, China; 2, Department of Mathematics, Xuzhou Normal University, Xuzhou, Jiangsu, 221116, China |
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| Abstract: | In this paper,the locally maximal ideals on posets a re introduced and examined.The existence of locally maximal ideals on posets is pr oved,and the following theorem is obtained:Every ideal of posets can be decompos ed as intersection of some locally maximal ideals.Specially,in the posets with d iscending chain condition of ideals,every ideal can be decomposed as finite inte rsection of locally maximal ideals. |
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| Keywords: | poset locally maximal ideal decomposition |
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