An Extension Theorem on Finitely Axiomatizable Algebraic Equation Systems
代数等式系有穷公理化的一个扩充定理

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.