Ring-like structures corresponding to generalized orthomodular lattices
Ivan Chajda, Helmut Länger, Maciej Mączyński · Czech digital mathematics library · 2004
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.