= Rng
{disambiguate=algebra}
{wiki}
= Nonunital ring
{synonym}
A rng has an <abelian group> under <addition>, an <associative> <multiplication>, and the <distributive property>; a multiplicative <identity element> is not required. Every <ring> under this wiki's unital convention is a rng. A <nonunital ring> may happen to have an identity: the terminology removes an axiom rather than imposing the absence of an identity. For example, the <even integers> with their usual operations have no multiplicative identity.
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