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:
“Back now to autumn, leaving the ended husk
Of summer that brought them here for Show Saturday
The men with hunters, dog-breeding wool-defined women,
Children all saddle-swank, mugfaced middleaged wives
Glaring at jellies, husbands on leave from the garden
Watchful as weasels, car-tuning curt-haired sons
Back now, all of them, to their local lives....”
—Philip Larkin (1922–1986)
“The boxer’s ring is the enjoyment of the part of society whose animal nature alone has been developed.”
—Ralph Waldo Emerson (1803–1882)