Bimodules

class sage.categories.bimodules.Bimodules(left_base, right_base, name=None)

Bases: sage.categories.category.CategoryWithParameters

The category of \((R,S)\)-bimodules

For \(R\) and \(S\) rings, a \((R,S)\)-bimodule \(X\) is a left \(R\)-module and right \(S\)-module such that the left and right actions commute: \(r*(x*s) = (r*x)*s\).

EXAMPLES:

sage: Bimodules(QQ, ZZ)
Category of bimodules over Rational Field on the left and Integer Ring on the right
sage: Bimodules(QQ, ZZ).super_categories()
[Category of left modules over Rational Field, Category of right modules over Integer Ring]
class ElementMethods
class Bimodules.ParentMethods
classmethod Bimodules.an_instance()

Return an instance of this class.

EXAMPLES:

sage: Bimodules.an_instance()
Category of bimodules over Rational Field on the left and Real Field with 53 bits of precision on the right
Bimodules.left_base_ring()

Return the left base ring over which elements of this category are defined.

EXAMPLES:

sage: Bimodules(QQ, ZZ).left_base_ring()
Rational Field
Bimodules.right_base_ring()

Return the right base ring over which elements of this category are defined.

EXAMPLES:

sage: Bimodules(QQ, ZZ).right_base_ring()
Integer Ring
Bimodules.super_categories()

EXAMPLES:

sage: Bimodules(QQ, ZZ).super_categories()
[Category of left modules over Rational Field, Category of right modules over Integer Ring]

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