Approximate distributive laws and finite equational bases for finite algebras in congruence-distributive varieties
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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.
2000 Mathematics Subject Classification.08B10 08A30 08B26
Keywords and phrases.congruence distributive principal congruence finite basis
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