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Equational bases for some varieties of orthomodular lattices related to states. (English) Zbl 0618.06003

In his former paper [Algebra Univers. 20, 368-396 (1985; Zbl 0581.06006)] the author studied varieties of orthomodular lattices which were determined by conditions on states. In this paper he considers equations valid in those varieties and shows that many of the varieties admit a recursive equational base. He also develops a constructive procedure for obtaining an equation valid in a given finite orthomodular lattice outside a variety.
Reviewer: P.Pták

MSC:

06C15 Complemented lattices, orthocomplemented lattices and posets
03C05 Equational classes, universal algebra in model theory
46L30 States of selfadjoint operator algebras
06B20 Varieties of lattices
08B05 Equational logic, Mal’tsev conditions
81P10 Logical foundations of quantum mechanics; quantum logic (quantum-theoretic aspects)

Citations:

Zbl 0581.06006
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References:

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