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Rees congruences in lattice-ordered algebras. (English) Zbl 0818.06005

A nonvoid subset \(S\) of a universal algebra \(A\) is called a Rees subset whenever the binary relation \(S\times S\cup \{\langle a,a\rangle; a\in A\backslash S\}\) is a congruence on \(A\); in this case \(S\times S\cup \{\langle a,a\rangle; a\in A\backslash\}\) is called a Rees congruence on \(A\). Rees sublattices of an arbitrary lattice were already characterized. Now the authors study more detailed properties of Rees sublattices in modular lattices of finite height and in bounded distributive lattices. Rees congruences on mono-unary algebras are described. Then applications in Heyting algebras, Ockham algebras and in pseudocomplemented lattices are achieved.
Reviewer: J.Duda (Brno)

MSC:

06B10 Lattice ideals, congruence relations
08A30 Subalgebras, congruence relations
06C05 Modular lattices, Desarguesian lattices
06D05 Structure and representation theory of distributive lattices
08A60 Unary algebras
06D20 Heyting algebras (lattice-theoretic aspects)
06D15 Pseudocomplemented lattices
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