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:
“To see ourselves as others see us can be eye-opening. To see others as sharing a nature with ourselves is the merest decency. But it is from the far more difficult achievement of seeing ourselves amongst others, as a local example of the forms human life has locally taken, a case among cases, a world among worlds, that the largeness of mind, without which objectivity is self- congratulation and tolerance a sham, comes.”
—Clifford Geertz (b. 1926)
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—Henry David Thoreau (1817–1862)