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

One generator

- 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 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.
- 4.
- 5.
- 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