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In the context of abstract algebra, a rng is a ring $\struct {R, +, \circ}$ which specifically does not have a unity.

That is, such that the semigroup $\struct {R, \circ}$ does not have an identity element.

The name arises from its nature as a ring with no identity element.

Linguistic Note

The word rng is a neologism (or possibly protologism), hence linguistic rules are to a certain extent arbitrary.

However, it is generally agreed that the word rng is pronounced rung.