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- Goldie's_theorem abstract "In mathematics, Goldie's theorem is a basic structural result in ring theory, proved by Alfred Goldie during the 1950s. What is now termed a right Goldie ring is a ring R that has finite uniform dimension (="finite rank") as a right module over itself, and satisfies the ascending chain condition on right annihilators of subsets of R. Goldie's theorem states that the semiprime right Goldie rings are precisely those that have a semisimple Artinian right classical ring of quotients. The structure of this ring of quotients is then completely determined by the Artin–Wedderburn theorem.In particular, Goldie's theorem applies to semiprime right Noetherian rings, since by definition right Noetherian rings have the ascending chain condition on all right ideals. This is sufficient to guarantee that a right-Noetherian ring is right Goldie. The converse does not hold: every right Ore domain is a right Goldie domain, and hence so is every commutative integral domain.A consequence of Goldie's theorem, again due to Goldie, is that every semiprime principal right ideal ring is isomorphic to a finite direct sum of prime principal right ideal rings. Every prime principal right ideal ring is isomorphic to a matrix ring over a right Ore domain.".
- Goldie's_theorem wikiPageExternalLink GoldieRing.html.
- Goldie's_theorem wikiPageExternalLink GoldiesTheorem.html.
- Goldie's_theorem wikiPageID "7738492".
- Goldie's_theorem wikiPageRevisionID "517349759".
- Goldie's_theorem hasPhotoCollection Goldie's_theorem.
- Goldie's_theorem subject Category:Ring_theory.
- Goldie's_theorem subject Category:Theorems_in_abstract_algebra.
- Goldie's_theorem type Abstraction100002137.
- Goldie's_theorem type Communication100033020.
- Goldie's_theorem type Message106598915.
- Goldie's_theorem type Proposition106750804.
- Goldie's_theorem type Statement106722453.
- Goldie's_theorem type Theorem106752293.
- Goldie's_theorem type TheoremsInAbstractAlgebra.
- Goldie's_theorem type TheoremsInAlgebra.
- Goldie's_theorem comment "In mathematics, Goldie's theorem is a basic structural result in ring theory, proved by Alfred Goldie during the 1950s. What is now termed a right Goldie ring is a ring R that has finite uniform dimension (="finite rank") as a right module over itself, and satisfies the ascending chain condition on right annihilators of subsets of R. Goldie's theorem states that the semiprime right Goldie rings are precisely those that have a semisimple Artinian right classical ring of quotients.".
- Goldie's_theorem label "Goldie's theorem".
- Goldie's_theorem sameAs m.026bfgw.
- Goldie's_theorem sameAs Q5580171.
- Goldie's_theorem sameAs Q5580171.
- Goldie's_theorem sameAs Goldie's_theorem.
- Goldie's_theorem wasDerivedFrom Goldie's_theorem?oldid=517349759.
- Goldie's_theorem isPrimaryTopicOf Goldie's_theorem.