ACTA MATHEMATICA UNIVERSITATIS COMENIANAE

ACTA MATHEMATICA UNIVERSITATIS COMENIANAE

Vol. LXXVI, (2007)
p. 231 - 240

Congruence kernels of orthoimplication algebras
I. Chajda, R. Halas and H. Laenger

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.

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

AMS Subject classification. Primary: 08A30, 20N02, 06A12, 06C15.

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Acta Mathematica Universitatis Comenianae
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