English Dictionary

ring

IPA（発音記号）

/ɹɪŋ/

名詞

(algebra) 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.

日本語の意味

環（かん）：代数学における代数的構造の一種。集合に対して二つの二項演算（加法と乗法）が定義され、加法についてはアーベル群となり、乗法についてはモノイドあるいは半群の構造を持ち、乗法が加法に分配される性質を持つ。

In abstract algebra, a ring provides a framework for studying polynomials and matrices under addition and multiplication.

抽象代数学では、加法についてアーベル群、乗法についてモノイドであり、乗法が加法に対して分配的であるような二つの二項演算を備えた集合から成る代数的構造（環）は、多項式や行列を加法と乗法の下で研究するための枠組みを提供する。

意味（1）

(algebra) 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.

The set of integers, ℤ, is the prototypical ring.

意味（2）

(algebra) 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.

The definition of ring without unity allows, for instance, the set 2ℤ of even integers to be a ring.

rings （ plural ）