PlanetMath: ideals in a Dedekind domain

(more info)

Math for the people, by the people.

Main Menu

sections Encyclopædia
Papers
Books
Expositions

meta Requests (198)
Orphanage
Unclass'd
Unproven (490)
Corrections (7)
Classification

talkback Polls
Forums
Feedback
Bug Reports

downloads Snapshots
PM Book

information News
Docs
Wiki
ChangeLog
TODO List
Legalese
About

Entry average rating: No information on entry rating

ideals in a Dedekind domain

(Theorem)

Let be a Dedekind domain, and let $\mathfrak{a}$ and $\mathfrak{b}$ be ideals of . Then there is an element $\omega$ and an ideal $\mathfrak{c}$ of such that

$\displaystyle \mathfrak{ac} = (\omega)$

and

$\displaystyle \mathfrak{b+c} = R.$

This result was proved by Steinitz in 1911.

"ideals in a Dedekind domain" is owned by yark. [ full author list (2) | owner history (1) ]

(view preamble)

See Also: divisor as factor of principal divisor

This object's parent.

Attachments:: two-generator property (Theorem) by pahio

Log in to rate this entry.
(view current ratings)

Cross-references: ideals, Dedekind domain
There is 1 reference to this entry.

This is version 6 of ideals in a Dedekind domain, born on 2002-07-03, modified 2008-04-29.
Object id is 3154, canonical name is EveryIdealInADedekindDomainIsAFactorOfAPrincipalIdeal.
Accessed 2392 times total.

Classification:

AMS MSC:	11R04 (Number theory :: Algebraic number theory: global fields :: Algebraic numbers; rings of algebraic integers)
	11R37 (Number theory :: Algebraic number theory: global fields :: Class field theory)

Pending Errata and Addenda

None.[ View all 4 ]

Discussion

forum policy

No messages.

Interact