A rng is a set $R$ together with two binary operations $+$ and $\cdot$ such that
- $R$ is an abelian group under $+$;
- $R$ is a semigroup under $\cdot$;
- $\cdot$ distributes over $+$: $a\cdot (b+c)=(a\cdot b) + (a\cdot c)$ and $(b+c)\cdot a = (b\cdot a) + (c\cdot a)$.
This is just a ring without a multiplicative identity.
Wikidata ID: Q17102802