“integral domain”的概念、定义、习题解题方法及翻译-数学辞典

单词

integral domain

释义

integral domain

A commutative ring R with identity, with the additional property that

(The axiom numbering follows on from that used for ring.) Thus an integral domain is a commutative ring with identity with no zero-divisors. The natural example is the set ℤ of all integers with the usual addition and multiplication. Any field is an integral domain. Further examples of integral domains (these are not fields) are: the set $inline$ of all real numbers of the form $inline$ , where a and b are integers, and the set R[x] of all polynomials in a variable x, with real coefficients, each with the normal addition and multiplication.

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