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Homotopy Type Theory
bimodule > history (changes)

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## Definiton

< bimodule

### A single action ring

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~~Let $R$ be a ring. An $R$-bimodule is an abelian group $B$ with a trilinear multiplicative $R$-biaction $(-)(-)(-):R \times B \times R \to B$.

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~~### Two different action rings

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~~Let $R$ and $S$ be rings. A $R$-$S$-bimodule is an abelian group $B$ with a trilinear multiplicative $R$-$S$-biaction $(-)(-)(-):R \times B \times S \to B$.

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~~## Properties

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- Every abelian group is a $\mathbb{Z}$-$\mathbb{Z}$-bimodule.
- Every left $R$-module is a $R$-$\mathbb{Z}$-bimodule.
- Every right $R$-module is a $\mathbb{Z}$-$R$-bimodule.

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~~## See also

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Last revised on June 13, 2022 at 06:06:05.
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