entries on finitely generated ideals

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

One

1. principal ideal

2. zero ideal

3. unit ideal

4. principal ideal ring

5. principal ideal domain

6. Bézout ring

7. divisibility by product

Two

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

1. invertible ideal is finitely generated

2. generators of inverse ideal

3. invertibility of regularly generated ideal (http://planetmath.org/InvertibilityOfRegularlyGeneratedIdeal)

4. Prüfer ring (http://planetmath.org/pruferring)

5. Prüfer domain (http://planetmath.org/pruferdomain)

6. ideal generators in Prüfer ring

7. finitely generated modules over a principal ideal domain

Formulae

1. well-definedness of product of finitely generated ideals

2. product of finitely generated ideals

3. cancellation ideal

4. ideal decomposition in Dedekind domain

5. ideal inverting in Prüfer ring

6. least common multiple

7. quotient of ideals

8. generators of a quotient polynomial ring

Title	entries on finitely generated ideals
Canonical name	EntriesOnFinitelyGeneratedIdeals
Date of creation	2015-05-06 15:39:55
Last modified on	2015-05-06 15:39:55
Owner	pahio (2872)
Last modified by	pahio (2872)
Numerical id	17
Author	pahio (2872)
Entry type	Topic
Classification	msc 13A15
Classification	msc 13C05
Classification	msc 16D25
Related topic	ProductOfFinitelyGeneratedIdeals
Related topic	TopicsOnIdeals