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
Famous quotes containing the words properties of, properties and/or rings:
“A drop of water has the properties of the sea, but cannot exhibit a storm. There is beauty of a concert, as well as of a flute; strength of a host, as well as of a hero.”
—Ralph Waldo Emerson (1803–1882)
“A drop of water has the properties of the sea, but cannot exhibit a storm. There is beauty of a concert, as well as of a flute; strength of a host, as well as of a hero.”
—Ralph Waldo Emerson (1803–1882)
“You held my hand
and were instant to explain
the three rings of danger.”
—Anne Sexton (1928–1974)