Wheel theory

A wheel is a type of algebra (in the sense of universal algebra) 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.

The term wheel is inspired by the topological picture ${\displaystyle \odot }$ of the real projective line together with an extra point ⊥ (bottom element) such that ${\displaystyle \bot =0/0}$.^[1]

A wheel can be regarded as the equivalent of a commutative ring (and semiring) where addition and multiplication are not a group but respectively a commutative monoid and a commutative monoid with involution.^[1]