Wheel theory
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Wheels are a kind of algebras where division is always defined. In particular, division by zero is meaningful. The real numbers can be extended to a wheel, as can any commutative ring.
Also the Riemann sphere can be extended to a wheel by adjoining an element <math>0/0<math>. The Riemann sphere is an extension of the complex plane by an element <math>\infty<math>, where <math>\frac{z}{0}=\infty<math> for any complex <math>z\neq 0<math>. However, <math>0/0<math> is still undefined on the Riemann sphere, but defined in wheels.
External link
Wheels --- On Division by Zero (http://www.math.su.se/~jesper/research/wheels/)