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高校应用数学学报
高校应用数学学报  2014, Vol. 29 Issue (4): 483-496    
    
每个元有上覆盖的紧生成格的结构
左凯, 王学平
四川师范大学 数学与软件科学学院, 四川成都 610066
The structures of compactly generated lattices in which every element has a cover
ZUO Kai, WANG Xue-ping
College of Mathematics and Software Science, Sichuan Normal University, Chengdu 610066, China
 全文: PDF 
摘要： Dilworth与Crawley1973年提出能否去掉上半模格条件来刻画元素的不可约完全交既分解问题以及能否去掉强原子格的条件刻画紧生成格结构的问题, 本文首先证明了每个元有上覆盖的紧生成格$L$中任意元有不可约完全交既分解, 从而肯定地回答了Dilworth与Crawley上述第一个问题. 之后, 在每个元有上覆盖的紧生成格中引入局部强模格与局部强分配格的概念, 研究了局部强模格中独立集的特性以及局部强模格与局部分配格的结构, 从而部分解决了Dilworth与Crawley上述第二个问题.
关键词： 紧生成格;  局部强模格;  上半模格;  原子格;  不可约完全交既分解;  独立集    
Abstract: This paper deals with two unsolved problems raised by Dilworth and Crawley in 1973. The first one is about the existence of irredundant completely meet decomposition for an element in compactly generated lattice which is not the upper semimodular lattice. The second one is about the structure of compactly generated lattice which is not the strongly atomic lattice. This paper first proves that every element which has a cover in the compactly generated lattice has an irredundant completely meet decomposition. Finally, the concepts of locally strong modular and locally strong distributive lattice are introduced. By investigating the structures of such lattices, this paper partly comes to the conclusion to the second problem.
Key words: compactly generated lattice    semimodular lattice    atomic lattice    locally strongly modular lattice    irredundant completely meet decomposition    independent set
收稿日期: 2014-02-12 出版日期: 2018-06-08
CLC:  O153.1  
基金资助: 国家自然科学基金(11171242)
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左凯
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引用本文:

左凯, 王学平. 每个元有上覆盖的紧生成格的结构[J]. 高校应用数学学报, 2014, 29(4): 483-496.

ZUO Kai, WANG Xue-ping. The structures of compactly generated lattices in which every element has a cover. Applied Mathematics A Journal of Chinese Universities, 2014, 29(4): 483-496.

链接本文:

http://www.zjujournals.com/amjcua/CN/    或    http://www.zjujournals.com/amjcua/CN/Y2014/V29/I4/483

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