Journal of Symbolic Logic

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

Christian Herrmann

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Abstract

For a finite von Neumann algebra factor M, the projections form a modular ortholattice L(M). We show that the equational theory of L(M) coincides with that of some resp. all L(ℂn × n) and is decidable. In contrast, the uniform word problem for the variety generated by all L(ℂn × n) is shown to be undecidable.

Article information

Source
J. Symbolic Logic, Volume 75, Issue 3 (2010), 1102-1110.

Dates
First available in Project Euclid: 9 July 2010

Permanent link to this document
https://projecteuclid.org/euclid.jsl/1278682219

Digital Object Identifier
doi:10.2178/jsl/1278682219

Mathematical Reviews number (MathSciNet)
MR2723786

Zentralblatt MATH identifier
1205.06005

Subjects
Primary: 06C20: Complemented modular lattices, continuous geometries 16E50: von Neumann regular rings and generalizations 16W10: Rings with involution; Lie, Jordan and other nonassociative structures [See also 17B60, 17C50, 46Kxx] 46L10: General theory of von Neumann algebras

Keywords
von Neumann algebra projection lattice continuous geometry equational theory

Citation

Herrmann, Christian. On the equational theory of projection lattices of finite von Neumann factors. J. Symbolic Logic 75 (2010), no. 3, 1102--1110. doi:10.2178/jsl/1278682219. https://projecteuclid.org/euclid.jsl/1278682219


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