Abstract
In this note it is shown that every von Neumann algebra has a semi modular projection lattice. The notions of a dual modular pair of projections and nonasymptoticity, which were shown by Mackey to coincide in a type ITM factor, are compared globally. A von Neumann algebra containing no asymptotic pairs of projections is characterized as the direct-sum of an abelian algebra and a finitedimensional algebra.
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