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Definability for equational theories of commutative groupoids

Jaroslav Ježek (2012)

Czechoslovak Mathematical Journal

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.

Diamond identities for relative congruences

Gábor Czédli (1995)

Archivum Mathematicum

For a class K of structures and A K let C o n * ( A ) resp. C o n K ( A ) denote the lattices of * -congruences resp. K -congruences of A , cf. Weaver [25]. Let C o n * ( K ) : = I { C o n * ( A ) : A K } where I is the operator of forming isomorphic copies, and C o n r ( K ) : = I { C o n K ( A ) : A K } . For an ordered algebra A the lattice of order congruences of A is denoted by C o n < ( A ) , and let C o n < ( K ) : = I { C o n < ( A ) : A K } if K is a class of ordered algebras. The operators of forming subdirect squares and direct products are denoted by Q s and P , respectively. Let λ be a lattice identity and let Σ be a set of lattice identities. Let Σ c λ ( r ; Q s , P ) denote...

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