Local Ring
In abstract algebra, more particularly in ring theory, local rings are certain rings that are comparatively simple, and serve to describe what is called "local behaviour", in the sense of functions defined on varieties or manifolds, or of algebraic number fields examined at a particular place, or prime. Local algebra is the branch of commutative algebra that studies local rings and their modules.
In practice, a commutative local ring often arises as the result of the localization of a ring at a prime ideal.
The concept of local rings was introduced by Wolfgang Krull in 1938 under the name Stellenringe. The English term local ring is due to Zariski.
Read more about Local Ring: Definition and First Consequences, Examples
Famous quotes containing the words local and/or ring:
“This is the only “wet” community in a wide area, and is the rendezvous of cow hands seeking to break the monotony of chuck wagon food and range life. Friday night is the “big time” for local cowboys, and consequently the calaboose is called the “Friday night jail.””
—Administration in the State of Texa, U.S. public relief program (1935-1943)
“Interpreting the dance: young women in white dancing in a ring can only be virgins; old women in black dancing in a ring can only be witches; but middle-aged women in colors, square dancing...?”
—Mason Cooley (b. 1927)