Bimodule

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Bimodule

Un A1-A2-bimodule est un ensemble M muni à la fois d'une structure de module à gauche sur un anneau A1 et d'une structure de module à droite sur un anneau A2 vérifiant

$\forall a \in A_1,\quad \forall x \in M,\quad \forall b \in A_2,\quad a.(x.b) = (a.x).b$.

Exemples

• Tout A-module à droite est aussi un $\mathbb Z$-A-bimodule
• A est un A-A bimodule
• Si A est commutatif, tout A-module peut être vu comme un A-A bimodule. Plus généralement, pour A quelconque, un A-module à gauche peut être vu comme un AAop bimodule.

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