摘要
主要给出了∩-弱完全分配格的并同态扩张的一个基本定理.
Definition. Suppose that Φ is a join-homomorphism of the lattice L into the lattice L1,then Φ is said to be completible if a subset Φ(s) = {Φ(x)| x∈s} of L1 has also the least upper bound which equals Φ (a) when a subset S of L has the least upper bound a.
Moreover above-mentioned join-homomorphism Φ is said to be complete ifL is a complete lattice and Φ is completive.
In this paper we mainly prove the following result
Theorem 1. If Φ is a completible join-homomorphism of the A weak complete distributive lattice L onto the A weak complete distributive lattice Ll, then
there exists one and only one complete join-homomorphism Φ from the completion L of L onto the completion L1 of L1 such that
Φ= Φ
in L
Corollary, if f is a isotone mapping of the rational number chain Q onto-the chain P without any covering element, then there exists one and only one
complete isotone mapping f from the closed real number chain onto the completion P of P such that
in Q.
出处
《江西科学》
1990年第4期18-23,共6页
Jiangxi Science
关键词
格论
η
弱完全分配格
并同态
A weak complete distributive lattice, Join-Homomorphism
