可补格按恒Ⅰ式集分类的问题(Ⅱ)

ON THE CLASSIFICATION OF COMPLEMENTED LATTICES ACCORDING TO THEIR TAUTOLOGIES Ⅱ.

本文是[1]的续篇。关于问题的含义以及有关概念与结果,都请参看该文,这里不再重复。本文讨论一种称为分组格的特殊可补格,得到了关于分组格按同型关系分类的一些初步结果。设 L 为一可补格,若存在 n 个子可补格 L1,…,Ln 适合:（i）每一 Li都含有0、I 以外的元。

This is a continuation of [1].In this article,we proved the following theorem: Theorem.Let L be a partitioned complemented lattice satisfying xx′=Ⅰ and xx′=0.Then a necessary and sufficient condition for L to be of the same type with a certain special partitioned complemented lattice C^k is that: (A_1)There exists a homomorphism from a complemented sublattice of L onto C^k;and (A_2)For each ξⅠ in L,there exists a homomorphism _ξ from L into C^k such that ξ(ξ)Ⅰ。 For relevant notions,see [1] and the present context.An outlined report of the results also appeared in Kexue Tongbao (Chinese edition),vol.25,no. 16(1980)。