Wheel theory

Wheel theory is the theory of wheels. A wheel is an algebraic structure where division by 0 has meaning. The term "wheel" was inspired by the topological picture formula_1.
Definition.
A wheel is an algebraic structure satisfying(for all values formula_2, formula_3, and formula_4):
Wheels replace the usual division with a applied to one argument formula_15 similar (but not identical) to the multiplicative inverse formula_16, such that formula_17 becomes shorthand for formula_18. Also, formula_19 replaces the fraction formula_20.