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