near-ring

In mathematics, a near-ring (also near ring or nearring) is an algebraic structure similar to a ring but satisfying fewer axioms. Near-rings arise naturally from functions on groups.

== Definition == A set N together with two binary operations + (called addition) and ⋅ (called multiplication) is called a (right) near-ring if: N is a group (not necessarily abelian) under addition; multiplication is associative (so N is a semigroup under multiplication); and multiplication on the right distributes over addition: for any x, y, z in N, it holds that (x + y)⋅z = (x⋅z) + (y⋅z).