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Congruence Kernels of Orthoimplication Algebras

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Author(s): I. Chajda | R. Halas | H. Laenger

Journal: Acta Mathematica Universitatis Comenianae
ISSN 0862-9544

Volume: LXXVI;
Issue: 2;
Start page: 231;
Date: 2007;
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Keywords: orthoimplication algebra | weakly regular | permutable at 1 | 3-permutable | orthomodular lattice | semi-orthomodular lattice | congruence | compatible congruence family | congruence kernel | p-filter | compatible filter family | relative pseudocomplement

ABSTRACT
Abstracting from certain properties of the implication operation in Boolean algebras leads to so-called orthoimplication algebras. These are in a natural one-to-one correspondence with families of compatible orthomodular lattices. It is proved that congruence kernels of orthoimplication algebras are in a natural one-to-one correspondence with families of compatible p-filters on the corresponding orthomodular lattices. Finally, it is proved that the lattice of all congruence kernels of an orthoimplication algebra is relatively pseudocomplemented and a simple description of the relative pseudocomplement is given.
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