Near-ring

Summary

A near-ring is a set with an addition and a multiplication that satisfies most of the ring axioms. Addition need not be commutative, and only one distributive law is required. The standard example is the set of all maps from a group to itself, with pointwise addition and composition. Near-rings stand to arbitrary maps of groups as rings stand to endomorphisms of abelian groups. They appear in the study of nonlinear maps, of permutation groups and of combinatorial designs.