Properties of Commutative Rings
For commutative rings, ideas of algebraic geometry make it natural to take a "small neighborhood" of a ring to be the localization at a prime ideal. A property is said to be local if it can be detected from the local rings. For instance, being a flat module over a commutative ring is a local property, but being a free module is not. See also Localization of a module.
Read more about this topic: Local Property
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