| 完全分配格上的一种对偶关系 |
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| 引用本文： | 樊太和.完全分配格上的一种对偶关系[J].陕西师范大学学报,1994(1). |
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| 作者姓名： | 樊太和 |
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| 作者单位： | 陕西师范大学数学系 |
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| 基金项目： | 国家教委回国人员资助费支持项目,陕西省自然科学基金 |
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| 摘 要： | 在完全分配格中引入了一种“＊”运算,利用这一运算,证明了对任一完全分配格中任一元素都可利用不小于等于它的元素的极小族来直接构造该元素的一个极大族,从而给出了极大族与极小族理论之间的内在联系．利用前面的结果,给出了完备集环上完全并素元之集与完全素元之集间的一一对应关系．
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| 关 键 词： | 分配格 ＊运算 极大族 极小族 |
A kind of duality on completely distributive lattices |
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| Fan Taihe.A kind of duality on completely distributive lattices[J].Journal of Shaanxi Normal University: Nat Sci Ed,1994(1). |
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| Authors: | Fan Taihe |
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| Abstract: | In the class of completely distributive lattices, an operation "*" is introduced. It is proved that for each element, a maximal family can be constructed by virtue of minimal families of those elements not less than nor equal to the element, hence an internal relation between minimal family and maximal family is obtained. As application, A natural one -toone correspondence between the set of all complete coprimes and the set of all complete primes of a complete ring of sets is obtained. |
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| Keywords: | distributive lattice "*" operation maximal family minimal family |
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