Rank ring
In mathematics, a rank ring is a ring with a real-valued rank function behaving like the rank of an endomorphism. introduced rank rings in his work on continuous geometry, and showed that the ring associated to a continuous geometry is a rank ring.Definition
defined a ring to be a rank ring if it is regular and has a real-valued rank function R with the following properties:
- 0 ≤ R ≤ 1 for all a
- R = 0 if and only if a = 0
- R = 1
- R ≤ R, R ≤ R
- If e2 = e, f2 = f, ef = fe = 0 then R = R + R.
