Commutative ring：Commutative ring

Commutative ring

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交換環

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在抽象代數之分支環論中，一個交換環（commutative ring）是乘法運算滿足交換律的環。對交換環的研究稱為交換代數學。 某些特定的交換環在下列類包含鏈中：.

說明

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Commutative Rings and Fields

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A commutative ring which has an identity element is called a commutative ring with identity. In a ring with identity, you usually also assume that $1 -ne 0$ . ( ...

Ring (mathematics)

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The simplest commutative rings are those that admit division by non-zero elements; such rings are called fields. Examples of commutative rings include the set ...

Commutative algebra

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Commutative algebra is essentially the study of the rings occurring in algebraic number theory and algebraic geometry. In algebraic number theory, the rings of ...

Graded

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In algebra, a graded-commutative ring is a graded ring that is commutative in the graded sense; that is, homogeneous elements x, y satisfy.

Category of rings

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The natural ring homomorphism from any commutative ring R to any one of its localizations is an epimorphism which is not necessarily surjective.

Ring theory

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In algebra, ring theory is the study of rings—algebraic structures in which addition and ... Commutative rings are much better understood than noncommutative ones.