On lattices of congruences of relational systems and universal algebras |
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Authors: | Jerzy P?onka |
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Institution: | (1) Polish Academy of Sciences, Wrocław, Poland |
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Abstract: | Let \(\mathfrak{X}\) =〈X;R〉 be a relational system.X is a non-empty set andR is a collection of subsets ofX α, α an ordinal. The system of equivalence relations onX having the substitution property with respect to members ofR form a complete latticeC( \(\mathfrak{X}\) ) containing the identity but not necessarilyX×X. It is shown that for any relational system (X;R) there is a groupoid definable onX whose congruence lattice isC( \(\mathfrak{X}\) )U{X×X} . Theorem 2 and Corollary 2 contain some interesting combinatorial pecularities associated with oriented complete graphs and simple groupoids. |
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Keywords: | Primary 08A05 Secondary 05C20 08A24 and phrases Relational systems groupoids congruence lattices |
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