Rng

Summary

A rng, also called a non-unital ring, is a structure with all the axioms of a ring except the existence of a multiplicative identity. The name is "ring" without the letter "i", for "identity". Rngs arise naturally: ideals, rings of functions with compact support, and many algebras in analysis have no unit element. Every rng embeds as an ideal in a ring with identity, so much of ring theory still applies.