class sage.categories.commutative_additive_groups.CommutativeAdditiveGroups(base_category)

The category of abelian groups, i.e. additive abelian monoids where each element has an inverse.

EXAMPLES:

sage: C = CommutativeAdditiveGroups(); C
Category of commutative additive groups
sage: C.super_categories()
[Category of additive groups, Category of commutative additive monoids]
sage: sorted(C.axioms())
True
True


Note

This category is currently empty. It’s left there for backward compatibility and because it is likely to grow in the future.

class Algebras(category, *args)
class CartesianProducts(category, *args)
class ElementMethods
additive_order()

Return the additive order of this element.

EXAMPLES:

sage: G = cartesian_product([Zmod(3), Zmod(6), Zmod(5)])
30
sage: any((i * G((1,1,1))).is_zero() for i in range(1,30))
False
sage: 30 * G((1,1,1))
(0, 0, 0)

sage: G = cartesian_product([ZZ, ZZ])