Rank ring

In mathematics, a rank ring is a ring with a real-valued rank function behaving like the rank of an endomorphism. (John von Neumann 1998) introduced rank rings in his work on continuous geometry, and showed that the ring associated to a continuous geometry is a rank ring.

John von Neumann (1998, p.231) defined a ring to be a rank ring if it is regular and has a real-valued rank function R with the following properties:

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