Associative algebras - Category Framework

Skip to content
Back to top
View this page
Edit this page

# Associative algebras

class sage.categories.associative_algebras.AssociativeAlgebras(base_category)

  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

    alias of `Algebras`