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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