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[parent] entries on finitely generated ideals (Topic)

This entry lists PlanetMath entries concerning finitely generated ideals of commutative rings.

One generator

  1. principal ideal
  2. principal ideal ring
  3. principal ideal domain
  4. Bézout ring
  5. divisibility by product

Two generators

  1. two-generator property
  2. multiplication rule gives inverse ideal
  3. invertibility of regularly generated ideal
  4. unique factorization and ideals in ring of integers

n generators

  1. invertible ideal is finitely generated
  2. generators of inverse ideal
  3. invertibility of regularly generated ideal
  4. Prüfer ring
  5. Prüfer domain
  6. ideal generators in Prüfer ring
  7. finitely generated modules over a principal ideal domain

Formulae

  1. product of finitely generated ideals
  2. cancellation ideal
  3. ideal decomposition in Dedekind domain
  4. ideal inverting in Prüfer ring
  5. least common multiple
  6. quotient of ideals



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See Also: product of finitely generated ideals, topics on ideals

Keywords:  commutative ring, finitely generated, finitely generated ideal

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Cross-references: quotient of ideals, least common multiple, ideal inverting in Prüfer ring, ideal decomposition in Dedekind domain, cancellation ideal, product of finitely generated ideals, finitely generated modules over a principal ideal domain, ideal generators in Prüfer ring, Prüfer domain, Prüfer ring, generators of inverse ideal, invertible ideal is finitely generated, unique factorization and ideals in ring of integers, invertibility of regularly generated ideal, multiplication rule gives inverse ideal, two-generator property, divisibility by product, Bézout ring, principal ideal domain, principal ideal ring, principal ideal, commutative rings, ideals, finitely generated, PlanetMath
There are 2 references to this entry.

This is version 9 of entries on finitely generated ideals, born on 2005-07-19, modified 2007-04-13.
Object id is 7244, canonical name is EntriesOnFinitelyGeneratedIdeals.
Accessed 1801 times total.

Classification:
AMS MSC: 16D25 (Associative rings and algebras :: Modules, bimodules and ideals :: Ideals)
 13C05 (Commutative rings and algebras :: Theory of modules and ideals :: Structure, classification theorems)
 13A15 (Commutative rings and algebras :: General commutative ring theory :: Ideals; multiplicative ideal theory)
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