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Chajda, Ivan; Länger, Helmut; Mączyński, Maciej

Ring-like structures corresponding to generalized orthomodular lattices. (English) Zbl 1068.06008

Math. Slovaca 54, No. 2, 143-150 (2004).
Summary: Ring-like structures, so-called Boolean pseudorings, that are in a natural bijective correspondence with generalized orthomodular lattices are defined. In contrast to generalized orthomodular lattices, Boolean pseudorings are universal algebras and form a variety which turns out to be arithmetical and congruence regular. Distributive Boolean pseudorings, resp. Boolean pseudorings with an associative addition operation are Boolean rings.

Cited in 2 Documents

MSC:

06C15 Complemented lattices, orthocomplemented lattices and posets
06E20 Ring-theoretic properties of Boolean algebras
08A30 Subalgebras, congruence relations

Keywords:

generalized orthomodular lattice; Boolean pseudoring; arithmetical; congruence regular; distributive; associative; Boolean ring
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References:

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