Associative algebras#

class sage.categories.associative_algebras.AssociativeAlgebras(base_category)[source]#

Bases: 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.

Warning

Until Issue #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.

EXAMPLES:

Sage

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

Python

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

Unital[source]#: alias of Algebras