Rings

class sage.categories.rings.Rings(s=None)

Bases: sage.categories.category.Category

The category of rings

Associative rings with unit, not necessarily commutative

EXAMPLES:

sage: Rings()
Category of rings
sage: Rings().super_categories()
[Category of rngs, Category of semirings]

TESTS:

sage: TestSuite(Rings()).run()

TODO (see: http://trac.sagemath.org/sage_trac/wiki/CategoriesRoadMap)

• Make Rings() into a subcategory or alias of Algebras(ZZ);
• A parent P in the category Rings() should automatically be in the category Algebras(P).

class ElementMethods

class Rings.HomCategory(category, name=None)

Bases: sage.categories.category.HomCategory

ParentMethods

alias of HomCategory.ParentMethods

extra_super_categories()

EXAMPLES:

sage: Rings().hom_category().extra_super_categories()
[Category of sets]

class Rings.ParentMethods

Rings.super_categories(*args, **kwds)

EXAMPLES:

sage: Rings().super_categories()
[Category of rngs, Category of semirings]