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

摘要

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(?~(n xn)) and is decidable. In contrast, the uniform word problem for the variety generated by all L(? ~(n xn)) is shown to be undecidable.