Noetherian ring - Wikipedia
WEBA Noetherian ring is a ring that satisfies the ascending chain condition on left and right ideals. Learn the definitions, properties, examples, and applications of Noetherian rings in mathematics.
Noetherian Ring -- from Wolfram MathWorld
WEBAug 22, 2024 · A Noetherian ring is a ring that satisfies the ascending chain condition on ideals, meaning that every ideal is finitely generated. Learn the equivalent conditions, the relation to Artinian rings, and the applications of Noetherian rings …
WEBLearn what a Noetherian ring is and how to check if a ring is Noetherian. See the proof of the key proposition that relates Noetherian rings and finitely generated modules, and some examples of Noetherian rings.
WEBA Noetherian ring is a commutative ring where every ideal is finitely generated. Learn the equivalent conditions, the ascending chain condition, and some examples of Noetherian and non-Noetherian rings.
WEBLearn the definition and properties of Noetherian rings and modules, and how to use short exact sequences to construct them. See examples of PIDs, Euclidean domains, polynomial rings and vector spaces that are Noetherian.
Noetherian ring - Encyclopedia of Mathematics
WEBApr 3, 2024 · A Noetherian ring is a ring that satisfies certain finiteness conditions on ideals or modules. Learn the definition, examples, properties and applications of Noetherian rings, named after E. Noether.
WEBLearn the definition, properties and examples of noetherian rings and modules, and how they relate to commutative algebras and vector spaces. See proofs of theorems, lemmas and corollaries using Hilbert basis, Artin-Tate and Zariski's lemmas.
WEBLearn about the Lasker-Noether Decomposition Theorem, which states that every proper ideal in a Noetherian ring can be expressed as an irredundant intersection of finitely many primary ideals. See definitions, examples, and proofs of related results.
WEBLearn the definition, properties and examples of Noetherian modules and rings, and how they relate to commutative algebra. The essay covers basic results, exercises, and proofs for readers with some familiarity with rings, ideals, and modules.
WEBExamples of Noetherian rings. So far the only rings we can easily prove are Noetherian are principal ideal domains, like Z and k[x], or finite. Our goal now is to develop theorems that enable us to create new Noetherian rings from old. Proposition.
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