Non-unital non-associative algebras

sage.categories.magmatic_algebras.MagmaticAlgebras

The category of algebras over a given base ring.

An algebra over a ring \(R\) is a module over \(R\) endowed with a bilinear multiplication.

Warning

MagmaticAlgebras will eventually replace the current Algebras for consistency with e.g. Wikipedia article Algebras which assumes neither associativity nor the existence of a unit (see trac ticket #15043).

EXAMPLES:

sage: from sage.categories.magmatic_algebras import MagmaticAlgebras
sage: C = MagmaticAlgebras(ZZ); C
Category of magmatic algebras over Integer Ring
sage: C.super_categories()
[Category of additive commutative additive associative additive unital distributive magmas and additive magmas,
 Category of modules over Integer Ring]