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.
"On the equational theory of projection lattices of finite von Neumann factors." J. Symbolic Logic 75 (3) 1102 - 1110, September 2010. https://doi.org/10.2178/jsl/1278682219