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Solvability of Generalized Orthomodular Lattices

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Orthomodular Lattices

Part of the book series: Mathematics and Its Applications () ((MAEE,volume 18))

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Abstract

Suppose K is a given equational class of lattices (cf. I.26) and let ‵L be a lattice. Denote by E K (‵L) the set formed by those congruences T on ‵L for which ‵L/T∈K. Since ‵L/U∈K for the universal congruence U=L}L, E K (‵L) ≠ ∅. Define C K to be the intersection ∩{T; T∈E K (‵L)}. Then C K (‵L) is a congruence on ‵L. From I.25 we conclude that ‵L/C K (‵L) is isomorphic to a subdirect product of the lattices ‵L/T where T runs over E K (‵L). By I.26, ‵L/C K (‵L)∈K.

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© 1985 Ladislav Beran, Prague

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Beran, L. (1985). Solvability of Generalized Orthomodular Lattices. In: Orthomodular Lattices. Mathematics and Its Applications (East European Series), vol 18. Springer, Dordrecht. https://doi.org/10.1007/978-94-009-5215-7_6

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  • DOI: https://doi.org/10.1007/978-94-009-5215-7_6

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-94-010-8807-7

  • Online ISBN: 978-94-009-5215-7

  • eBook Packages: Springer Book Archive

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