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# Integral domains

class `sage.categories.integral_domains.``IntegralDomains`(base_category)

  Bases: `sage.categories.category_with_axiom.CategoryWithAxiom_singleton`

  The category of integral domains

  An integral domain is commutative ring with no zero divisors, or equivalently a commutative domain.

  EXAMPLES:

      sage: C = IntegralDomains(); C
      Category of integral domains
      sage: sorted(C.super_categories(), key=str)
      [Category of commutative rings, Category of domains]
      sage: C is Domains().Commutative()
      True
      sage: C is Rings().Commutative().NoZeroDivisors()
      True

  TESTS:

      sage: TestSuite(C).run()

  class `ElementMethods`
  class `IntegralDomains.``ParentMethods`
    `is_integral_domain`()

      Return True, since this in an object of the category of integral domains.

      EXAMPLES:

          sage: QQ.is_integral_domain()
          True
          sage: Parent(QQ,category=IntegralDomains()).is_integral_domain()
          True

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