Author | Beran, Ladislav. author |
---|---|
Title | Orthomodular Lattices [electronic resource] : Algebraic Approach / by Ladislav Beran |
Imprint | Dordrecht : Springer Netherlands, 1985 |
Connect to | http://dx.doi.org/10.1007/978-94-009-5215-7 |
Descript | XX, 394 p. online resource |
I: Introduction -- II: Elementary Theory of Orthomodular Lattices -- 1. Ortholattices -- 2. Commutativity -- 3. Orthomodular lattices -- 4. Properties of commutativity in orthomodular lattices -- 5. Characteristic properties of orthomodular lattices -- 6. Interval algebra -- Exercises -- III: Structure of Orthomodular Lattices -- 1. Skew operations -- 2. Free orthomodular lattice F2 -- 3. Introduction to Hilbert spaces -- 4. Projection lattice of a Hilbert space -- Exercises -- IV: Amalgams -- 1. Amalgams of posets -- 2. Amalgams of lattices -- 3. Amalgams of orthomodular lattices -- 4. Atomic amalgams of Boolean algebras -- Exercises -- V: Generalized Orthomodular Lattices -- 1. Orthogonality relation -- 2. Janowitzโs embedding -- 3. Congruence relations -- 4. Congruence relations and p-ideals -- 5. Commutators -- Exercises -- VI: Solvability of Generalized Orthomodular Lattices -- 1. Reflective and coreflective congruences -- 2. Projective allelomorph -- 3. Commutator sublattices -- 4. Solvability in equational classes of lattices -- Exercises -- VII: Special Properties of Orthomodularity -- 1. Commutators of n elements -- 2. Finitely generated orthomodular lattices -- 3. Formulas for orthomodular lattices -- 4. Exchange theorems -- 5. Center of an orthomodular lattice -- 6. Identities and operations -- 7. Analogues of Foulis-Holland Theorem -- Exercises -- VIII: Application -- 1. Orthomodularity and experimental propositions -- 2. Compatibility -- 3. Dimension theory -- 4. Orthologics -- Exercises -- Answers to Exercises -- Solutions to Exercises of Chapter II -- Solutions to Exercises of Chapter III -- Solutions to Exercises of Chapter IV -- Solutions to Exercises of Chapter V -- Solutions to Exercises of Chapter VI -- Solutions to Exercises of Chapter VII -- Solutions to Exercises of Chapter VIII -- References