关于l－群的半单结构

令Ｇ是一个ｌ－群，Ｇ的一个凸ｌ－子群Ａ叫做多余的，如果对Ｇ的任－凸ｌ－子群Ｗ，只要Ａ∨Ｗ＝Ｇ，就有Ｗ＝Ｇ．复令Ｒ（Ｇ）为Ｇ的所有多余凸ｌ－子群的集合并生成的凸ｌ－子群．我们证明了Ｒ（Ｇ）是ｌ－群Ｇ的一种报并且是在Ａｍｉｔｓｕｒ－Ｋｕｒｏｓｈ意义下的根．进一步我们得到了有限值ｌ－群的半单结构定理即Ｒ（Ｇ）＝０当且仅当Ｇｌ－同构于具有半单性的单ｌ－群的亚直积，同时我们还得到了一系列有意义的推论．

On the Semisimple Structure of l-groups

Let Gbe an l-group,one convex l-subgroup A of G is said to be superfluous, if A∨V W = G for an arbitary convex l-subgroup W of G, then W = G. Again let R(G) be the convex l-subgroup which is generated by the union of all superfluous convex subgroups of G. We prove that R(G) is one kind of radical of l-group G in Amitsur-Kurosh sence. Furthermore, we obtain the semisimple structure theorem for finite-valued l-groups,i.e. R(G) = 0 iff G is l-isomorphic to a subdirect product of simple l-groups with semisimplicity. Moreover, we also obtain some important corollaries.