Journal of Symbolic Logic

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

Christian Herrmann

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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

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

First available in Project Euclid: 9 July 2010

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

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

von Neumann algebra projection lattice continuous geometry equational theory


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.

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