Filtered Algebras With Basis

A filtered algebra with basis over a commutative ring \(R\) is a filtered algebra over \(R\) endowed with the structure of a filtered module with basis (with the same underlying filtered-module structure). See FilteredAlgebras and FilteredModulesWithBasis for these two notions.

sage.categories.filtered_algebras_with_basis.FilteredAlgebrasWithBasis

The category of filtered algebras with a distinguished homogeneous basis.

A filtered algebra with basis over a commutative ring \(R\) is a filtered algebra over \(R\) endowed with the structure of a filtered module with basis (with the same underlying filtered-module structure). See FilteredAlgebras and FilteredModulesWithBasis for these two notions.

EXAMPLES:

sage: C = AlgebrasWithBasis(ZZ).Filtered(); C
Category of filtered algebras with basis over Integer Ring
sage: sorted(C.super_categories(), key=str)
[Category of algebras with basis over Integer Ring,
 Category of filtered algebras over Integer Ring,
 Category of filtered modules with basis over Integer Ring]