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Definability for equational theories of commutative groupoids

Jaroslav Ježek (2012)

Czechoslovak Mathematical Journal

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We find several large classes of equations with the property that every automorphism of the lattice of equational theories of commutative groupoids fixes any equational theory generated by such equations, and every equational theory generated by finitely many such equations is a definable element of the lattice. We conjecture that the lattice has no non-identical automorphisms.

The ordering of commutative terms

Jaroslav Ježek (2006)

Czechoslovak Mathematical Journal

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By a commutative term we mean an element of the free commutative groupoid F of infinite rank. For two commutative terms a , b write a b if b contains a subterm that is a substitution instance of a . With respect to this relation, F is a quasiordered set which becomes an ordered set after the appropriate factorization. We study definability in this ordered set. Among other things, we prove that every commutative term (or its block in the factor) is a definable element. Consequently, the ordered...