| 偏序集的代数完备 |
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| 引用本文： | 黄梦桥,李庆国.偏序集的代数完备[J].模糊系统与数学,2009,23(3). |
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| 作者姓名： | 黄梦桥 李庆国 |
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| 作者单位： | 1. 湖南涉外经济学院,湖南,长沙,410205;湖南大学,数学与计量经济学院,湖南,长沙,410082
2. 湖南大学,数学与计量经济学院,湖南,长沙,410082 |
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| 基金项目： | 国家自然科学基金资助项目 |
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| 摘 要： | 引进一个偏序集的代数完备, 并且构造任意偏序集的一个代数完备.有最小元的并半格的代数完备正好是它的理想完备. 一个偏序集的代数完备同构于它的一个由下集作为元的完备格,并且这个完备格包含所有主理想. 基于代数完备的Galois联络的下扩张仍然是一个Galois联络.
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| 关 键 词： | 代数完备 理想完备 下扩张 |
The Algebraic Completion of Posets |
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| HUANG Meng-qiao,LI Qing-guo.The Algebraic Completion of Posets[J].Fuzzy Systems and Mathematics,2009,23(3). |
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| Authors: | HUANG Meng-qiao LI Qing-guo |
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| Institution: | 1.Hunan International Economics University;Changsha 410205;China;2.Mathematics and Econometrics College;Hunan University;Changsha 410082;China |
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| Abstract: | This paper introduces the notion of algebraic completion of a poset and constructs a concrete algebraic completion of a poset.An ideal completion of P is just an algebraic completion of P whenever P is a join semilattice with a bottom.An algebraic completion of a poset P could be represented by a down-set algebraic lattice which contains all principal ideals.The lower extension of a Galois connection is again a Galois connection based on algebraic completion. |
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| Keywords: | Algebraic Completion Ideal Completion Lower Extension |
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