Approximate distributive laws and finite equational bases for finite algebras in congruence-distributive varieties

摘要

For a congruence-distributive variety, Maltsev’s construction of principal congruence relations is shown to lead to approximate distributive laws in the lattice of equivalence relations on each member. As an application, in the case of a variety generated by a finite algebra, these approximate laws yield two known results: the boundedness of the complexity of unary polynomials needed in Maltsev’s construction and the finite equational basis theorem for such a variety of finite type. An algorithmic version of the construction is included.