格序群的极子群在凸l－子群格中生成的闭子格

The Complete Sublattice of the Lattice of Convex L-Subgroups of An L-Group Generated by Its Polar Subgroups

设Ｇ是一个格序群，Ｐ（Ｇ）是Ｇ的极子群集合，Ｃ（Ｇ）是Ｇ的凸ｌ－子群集合，Ω（Ｇ）是Ｐ（Ｇ）在Ｃ（Ｇ）中生成的闭子格，本文通过对Ω（Ｇ）的研究得到了一系列重要结果，对有限值格序群给予了一系列新的刻画，证明了ｇ是基元当且仅当ｇ－是ｇ的唯一的Ω－值等结论，实际上对Ｐ．Ｃｏｎｒａｄ提出的问题＂Ｄｅｓｃｒｉｂｅｔｈｅｅｌｅｍｅｎｔｓｉｎ＂进行了富有意义的探索。

In this paper, letting G be an L-group, P(G) the set of the polar subgroups ofG, C(G) the lattice of convex L- subgroups of G and n(G) the complete sublattice Of C (G)generated by P(G), some research work has been done on n (G) and then a lot of important results were obtained. Through a series of new description of the finite valued L-groups conclusions were drawn that g is a basic element when and only when g is the unique vaule of g,which really is a valuable inquiry about the problem ' Describe the elements in 'proposed byP. Conrad.