Rings¶
-
sage.categories.rings.
Rings
¶ The category of rings
Associative rings with unit, not necessarily commutative
EXAMPLES:
sage: Rings() Category of rings sage: sorted(Rings().super_categories(), key=str) [Category of rngs, Category of semirings] sage: sorted(Rings().axioms()) ['AdditiveAssociative', 'AdditiveCommutative', 'AdditiveInverse', 'AdditiveUnital', 'Associative', 'Distributive', 'Unital'] sage: Rings() is (CommutativeAdditiveGroups() & Monoids()).Distributive() True sage: Rings() is Rngs().Unital() True sage: Rings() is Semirings().AdditiveInverse() True
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 categoryAlgebras(P)
.