What is "rng"

n. (context algebra English) An algebraic structure satisfying the same properties as a ring, except that multiplication need not have an identity element.

Rng or RNG may refer to:

In mathematics, and more specifically in abstract algebra, a rng (or pseudo-ring or non-unital ring) is an algebraic structure satisfying the same properties as a ring, without assuming the existence of a multiplicative identity. The term "rng" (pronounced rung) is meant to suggest that it is a "ring" without "i", i.e. without the requirement for an "identity element".

There is no consensus in the community as to whether the existence of a multiplicative identity must be one of the ring axioms (see the history section of the article on rings). The term "rng" was coined to alleviate this ambiguity when people want to refer explicitly to a ring without the axiom of multiplicative identity.

A number of algebras of functions considered in analysis are not unital, for instance the algebra of functions decreasing to zero at infinity, especially those with compact support on some (non- compact) space.