一致极小对,一致有界性及有穷基定理

本文使用最小板块的思想，揭示了泛代数领域中任一分配簇的任一代数都具有两个性质；（１）投射意义下一致极小对是存在的。（２）存在相对于整个族而言的极小对投射的一致上界。用以上的结果，给出了著名的有穷基定理的一个简单的、构造性的证明。

Uniformly Minimal Pair, Unoform Bonndness andthe Finite Base Theorem

By using the idea of so-called minimal blocks as a medium, we are able to provethe following two conclusions: (1) given any congruence-distributive variety in any algebra of therelated variety, there exists under projectivity a uniform minimal pair for each principal congru-ence.(2) For this variety, there exists a uniform boundness on the lengths of the projectivities.Furthermore, as a simple consequence of above results we readily provide a relatively short, prooffor the famous Finite Base Theorem.