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algebra > commutative algebra > commutative ring > integral domain
... > algebra > abstract algebra > algebraic structure > ring theory > ring > commutative ring > integral domain

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integral domain  

Definition

  • In mathematics, specifically abstract algebra, an integral domain is a nonzero commutative ring in which the product of any two nonzero elements is nonzero. Integral domains are generalizations of the ring of integers and provide a natural setting for studying divisibility. In an integral domain, every nonzero element a has the cancellation property, that is, if a ≠ 0, an equality ab = ac implies b = c.
    (Wikipedia, The Free Encyclopedia, https://en.wikipedia.org/wiki/Integral_domain)

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http://data.loterre.fr/ark:/67375/PSR-N11QQH4B-1

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