PlanetMath: flat module

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flat module

(Definition)

A right module over a ring is flat if the tensor product functor $M \otimes_R (-)$ is an exact functor.

Similarly, a left module over is flat if the tensor product functor $(-) \otimes_R N$ is an exact functor.

"flat module" is owned by antizeus.

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Other names:

flat

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Cross-references: exact functor, functor, tensor product, ring, right module
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This is version 2 of flat module, born on 2002-01-05, modified 2003-09-14.
Object id is 1369, canonical name is FlatModule.
Accessed 4895 times total.

Classification:

16D40 (Associative rings and algebras :: Modules, bimodules and ideals :: Free, projective, and flat modules and ideals)

Pending Errata and Addenda

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