| 完备格的商格的分配性 |
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| 引用本文： | 曾群.完备格的商格的分配性[J].南昌大学学报(工科版),1991,13(4):1. |
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| 作者姓名： | 曾群 |
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| 作者单位： | 江西工业大学基础课部； |
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| 摘 要： | 本文利用对任意交封闭的完备格上的同余关系得到了一个与商格同构的完备格的序子格。利用该序子格为交闭子格的附加条件,得到了商格满足原完备格所具有的分配性的统一条件。另外,还证明了完全分配格的完备同态象必同构于它自身的一个序子格。
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| 关 键 词： | 序子格 完备格 分配性 商格 交同余关系 |
The Distributivity of Quotient Lattices |
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| Zeng Qun.The Distributivity of Quotient Lattices[J].Journal of Nanchang University(Engineering & Technology Edition),1991,13(4):1. |
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| Authors: | Zeng Qun |
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| Affiliation: | Basic Courses Department |
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| Abstract: | In this paper, define in a complete lattice a meet-closed congruence relation, which brings about for the complete lattice an order sublattice isomorphic to the quotient lattice of the meet-closed congruence relation. with this order Sublattice of the complete lattice, we obtain a uniform sufficient condition for the quotient lattice to maintain the distributivity of the complete lattice. Moreover, we proof that any complete homomorphie image of a complete lattice is isomorphic to one of its own order sublattices. |
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| Keywords: | Complete lattices Meet-closed congruence relations Quotient Lattices Distributivity |
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