Integral domains#
- class sage.categories.integral_domains.IntegralDomains(base_category)#
Bases:
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
- class ElementMethods#
Bases:
object
- class ParentMethods#
Bases:
object
- is_integral_domain(proof=True)#
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 sage: L.<z> = LazyLaurentSeriesRing(QQ) sage: L.is_integral_domain() True sage: L.is_integral_domain(proof=True) True