absolutely flat

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:

• Boolean rings are flat.

• Homomorphic images of absolutely flat rings are flat.

• Absolutely flat local rings are fields.

• In absolutely flat rings, non-units are zero divisors.

Title	absolutely flat
Canonical name	AbsolutelyFlat
Date of creation	2013-03-22 14:35:52
Last modified on	2013-03-22 14:35:52
Owner	mathcam (2727)
Last modified by	mathcam (2727)
Numerical id	5
Author	mathcam (2727)
Entry type	Definition
Classification	msc 16D40