代数等式系有穷公理化的一个扩充定理

An Extension Theorem on Finitely Axiomatizable Algebraic Equation Systems

首先介绍两个概念：主同余类的弱可定义性以及次直不可分解类的可定义性．证明了任一有穷代数Ａ，若Ｖ（Ａ）具有弱可定义的主同余类以及可定义次直不可分解类，则它的等式系是可以有穷公理化的．进一步的讨论揭示出其结果是新的，是对已有工作的有意义的扩充．

First, the two notions: weakly definable principal congruence and definable subdirectly irreducible class are introduced in this paper. The authors prove that if a variety generated by a finite algebra has both weakly definable principal congruence and definable subdirectly irreducible class, its equational system is finitely axiomatizable. Further discussion shows that the results are new, and are significant generalization of the known results.