On the equational theory of projection lattices of finite von neumann factors

DOI10.2178/jsl/1278682219zbMath1205.06005OpenAlexW2005115893MaRDI QIDQ4931110

Christian Herrmann

Publication date: 4 October 2010

Published in: The Journal of Symbolic Logic (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.2178/jsl/1278682219

zbMATH Keywords

von Neumann algebraequational theorycontinuous geometryprojection lattice

Mathematics Subject Classification ID

General theory of von Neumann algebras (46L10) Rings with involution; Lie, Jordan and other nonassociative structures (16W10) Complemented modular lattices, continuous geometries (06C20) von Neumann regular rings and generalizations (associative algebraic aspects) (16E50)

Related Items (7)

Decidability of the equational theory of the continuous geometry \(\mathrm{CG}(\mathbb F)\) ⋮ Quantum logic is undecidable ⋮ Three ultrafilters in a modular logic ⋮ On geometric representations of modular ortholattices ⋮ On varieties of modular ortholattices that are generated by their finite-dimensional members. ⋮ Unit-regularity and representability for semiartinian $*$-regular rings ⋮ On the complexity of equational decision problems for finite height complemented and orthocomplemented modular lattices

Cites Work

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• The regular ring of a finite AW\(^*\)-algebra
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• The maximal ring of quotients of a finite von Neumann algebra
• Quadratic forms in infinite dimensional vector spaces
• Quantum logic in algebraic approach
• On \(n\)-distributive modular ortholattices
• On rings of operators
• The logic of quantum mechanics
• Continuous geometries with a transition probability
• Quantum logic as motivated by quantum computing

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