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absolutely flat (Definition)

A ring $ A$ is absolutely flat if every module over $ A$ is flat.

For commutative rings with unity, a ring is absolutely flat if and only if every principal ideal is idempotent.

Some properties:

Bibliography

1
Introduction to Commutative Algebra, by Atiyah and MacDonald.



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Cross-references: zero divisors, fields, local rings, homomorphic images, Boolean rings, properties, idempotent, principal ideal, unity, commutative rings, flat, module, ring

This is version 2 of absolutely flat, born on 2004-09-13, modified 2005-03-18.
Object id is 6166, canonical name is AbsolutelyFlat.
Accessed 1479 times total.

Classification:
AMS MSC: 16D40 (Associative rings and algebras :: Modules, bimodules and ideals :: Free, projective, and flat modules and ideals)
Pending Errata and Addenda
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