### Navigation

- index
- modules |
- next |
- previous |
- Category Theory »

# Unique factorization domains

class `sage.categories.unique_factorization_domains.``UniqueFactorizationDomains`(s=None)

  Bases: `sage.categories.category_singleton.Category_singleton`

  The category of unique factorization domains constructive unique factorization domains, i.e. where one can constructively factor members into a product of a finite number of irreducible elements

  EXAMPLES:

      sage: UniqueFactorizationDomains()
      Category of unique factorization domains
      sage: UniqueFactorizationDomains().super_categories()
      [Category of gcd domains]

  TESTS:

      sage: TestSuite(UniqueFactorizationDomains()).run()

  class `ElementMethods`
  class `UniqueFactorizationDomains.``ParentMethods`
    `is_unique_factorization_domain`()

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

      EXAMPLES:

          sage: Parent(QQ,category=UniqueFactorizationDomains()).is_unique_factorization_domain()
          True

  `UniqueFactorizationDomains.``additional_structure`()

    Return whether `self` is a structure category.

    See also

    `Category.additional_structure()`

    The category of unique factorization domains does not define additional structure: a ring morphism between unique factorization domains is a unique factorization domain morphism.

    EXAMPLES:

        sage: UniqueFactorizationDomains().additional_structure()

  `UniqueFactorizationDomains.``super_categories`()

    EXAMPLES:

        sage: UniqueFactorizationDomains().super_categories()
        [Category of gcd domains]

### Navigation

- index
- modules |
- next |
- previous |
- Category Theory »