l-群的主极子群格的极小条件  

Minimal Condition of the Lattice of All Principal Polar Subgroups of an l-group

作　　者：吕新民[1] 

机构地区：[1]南方冶金学院理学系,江西赣州341000

出　　处：《南方冶金学院学报》2001年第1期46-50,共5页Journal of Southern Institute of Metallurgy

摘　　要：研究了的ｌ－群Ｇ的主极子群格ＰＰ（Ｇ）的极小条件，主要证明了ＰＰ（Ｇ）满足极小条件当且仅当对于　Ｎ∈Ｐｍ（Ｇ），Ｎ＝ａ．作为应用，还证明了：（１）Ｇ是紧生成的ｌ－群，Ｆｖ与Ｆｖ是等价的；（２）Ｇ是有基的ｌ－群，则Ｐ（Ｇ）格是完全分配的．Minimal condition of the lattice PP(G) of all principal polar subgroups of an l-group G is studied, the main result that PP(G) satisfies minimal condition if and only if for any N ∈Pm (G), N=a is proved. As for its application, We also prove: (1) if G is compactly generated, Fv andFv: are equivalent. (2) if G has a basis, P(G) is completely distributive lattice.

关 键 词：L-群 主极子群格 极小条件 极小素子群 

分 类 号：O152[理学—数学]