Generalizing von Neumann’s result on type II $_1$ von Neumann algebras, I characterise lattice isomorphisms between projection lattices of arbitrary von Neumann algebras by means of ring isomorphisms between the algebras of locally measurable operators. Moreover, I give a complete description of ring isomorphisms of locally measurable operator algebras when the von Neumann algebras are without type II direct summands.

中文翻译：

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冯诺依曼代数投影格间的格同构

在类型 II 上推广冯诺依曼的结果 $_1$ von Neumann algebras，我通过局部可测算子的代数之间的环同构来表征任意 von Neumann 代数的投影格之间的格同构。此外，当冯诺依曼代数没有II型直接和时，我给出了局部可测算子代数的环同构的完整描述。