Near-Ring

A near-ring is a set N equipped with two operations, addition (+) making (N, +) a (usually noncommutative) group or at least a group-like structure, and a multiplication (·) that is associative, where one distributive law holds (typically right distributivity: (a + b)·c = a·c + b·c) but the other may fail; definitions vary on whether additively the structure must be a group or just a monoid.