The logic induced by a system of homomorphisms and its various algebraic characterizations. (English) Zbl 0879.06005

Dorninger, Dietmar; Länger, Helmut; Mączyński, Maciej

Demonstr. Math. 30, No. 1, 215-232 (1997).

The authors first find a variant of the inverse spectral theorem for homomorphisms of certain algebraic systems, generalizing in a way the standard spectral theorem for Hilbert spaces. Then they apply this result to obtain an interesting equivalence between ring-like structures and lattices, a main result being the isomorphism of a class of Boolean quasirings and orthomodular lattices.

Reviewer: P.Pták (Praha)

MSC:

06C15	Complemented lattices, orthocomplemented lattices and posets
03G12	Quantum logic
06E20	Ring-theoretic properties of Boolean algebras
81P10	Logical foundations of quantum mechanics; quantum logic (quantum-theoretic aspects)

Keywords:

inverse spectral theorem; ring-like structures; Boolean quasirings; orthomodular lattices