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bimodule (Definition)

Let R and S be rings. An (R,S)-bimodule is an abelian group M which is a left module over R and a right module over S such that the r(ms)=(rm)s holds for each r in R, m in M, and s in S. Equivalently, M is an (R,S)-bimodule if it is a left module over $R\otimes\opposite{S}$ or a right module over $\opposite{R}\otimes S$ .

When M is an (R,S)-bimodule, we sometimes indicate this by writing the module as ${}_RM_S$ .

If P is a subgroup of M which is also an (R,S)-bimodule, then P is an (R,S)-subbimodule of M.




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"bimodule" is owned by mps. [ full author list (2) | owner history (1) ]
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Other names:  sub-bimodule
Also defines:  subbimodule
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Cross-references: subgroup, module, left module, abelian group, rings
There are 7 references to this entry.

This is version 5 of bimodule, born on 2001-11-23, modified 2007-06-25.
Object id is 987, canonical name is Bimodule.
Accessed 5610 times total.

Classification:
AMS MSC16D20 (Associative rings and algebras :: Modules, bimodules and ideals :: Bimodules)

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