Abstract
Does every finite algebraic system A with finitely many operations possess a finite list of polynomial identities (laws), valid in A, from which all other such identities follow? Surprisingly, no ( R. C. Lyndon, 1954). The answer is, however, affirmative for various particular kinds of algebraic systems, such as finite groups (Oates and Powell), finite lattices, and even finite lattice-ordered algebraic systems (McKenzie). The purpose of the present paper is to provide a sufficient condition that guarantees an affirmative answer without referring to any particular kind of operation: It is sufficient for A to be a finite member of an equational class of algebraic systems whose congruence lattices are distributive. The proof is constructive. Applications include the case of lattice-ordered algebraic systems.
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