In algebra, particularly in the context of ring theory, the term "rng" (pronounced "ring") is an abbreviation that refers to a mathematical structure that is similar to a ring but does not necessarily require the existence of a multiplicative identity (i.e., an element that acts as 1 in multiplication).
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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.