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 .

 Definition 
A wheel is an algebraic structure satisfying(for all values , , and ):

 Addition and multiplication are commutative and associative, with  and  as their respective identities.









Wheels replace the usual division with a unary operator applied to one argument  similar (but not identical) to the multiplicative inverse , such that  becomes shorthand for . Also,  replaces the fraction .

Sources
Carlström, Jesper: . Mathematical Structures in Computer Science, 14(2004): no. 1, 143–184 (also available online here ).

References

Category:Abstract algebra