Associative algebras#

class sage.categories.associative_algebras.AssociativeAlgebras(base_category)#

Bases: sage.categories.category_with_axiom.CategoryWithAxiom_over_base_ring

The category of associative algebras over a given base ring.

An associative algebra over a ring \(R\) is a module over \(R\) which is also a not necessarily unital ring.


Until trac ticket #15043 is implemented, Algebras is the category of associative unital algebras; thus, unlike the name suggests, AssociativeAlgebras is not a subcategory of Algebras but of MagmaticAlgebras.


sage: from sage.categories.associative_algebras import AssociativeAlgebras
sage: C = AssociativeAlgebras(ZZ); C
Category of associative algebras over Integer Ring

alias of sage.categories.algebras.Algebras