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:
“The local is a shabby thing. There’s nothing worse than bringing us back down to our own little corner, our own territory, the radiant promiscuity of the face to face. A culture which has taken the risk of the universal, must perish by the universal.”
—Jean Baudrillard (b. 1929)
“I started out very quiet and I beat Turgenev. Then I trained hard and I beat de Maupassant. I’ve fought two draws with Stendhal, and I think I had an edge in the last one. But nobody’s going to get me in any ring with Tolstoy unless I’m crazy or I keep getting better.”
—Ernest Hemingway (1899–1961)