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

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