ring

Language: EN · Kind: word · Transcription: [/ɹɪŋ/]

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Senses

1. ring (noun) — sense 1

Definition: An algebraic structure which consists of a set with two binary operations: an additive operation and a multiplicative operation, such that the set is an abelian group under the additive operation, a monoid under the multiplicative operation, and such that the multiplicative operation is distributive with respect to the additive operation.

Example: The set of integers, #92;mathbb#123;Z#125;, is the prototypical ring.

2. ring (noun) — sense 2

Definition: An algebraic structure as above, but only required to be a semigroup under the multiplicative operation, that is, there need not be a multiplicative identity element.

Example: The definition of ring without unity allows, for instance, the set 2#92;mathbb#123;Z#125; of even integers to be a ring.

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