Principal ideal domain
In mathematics, a principal ideal domain, or PID, is an integral domain in which every ideal is principal, i.e., can be generated by a single element. More generally, a principal ideal ring is a nonzero commutative ring whose ideals are principal, although some authors (e.g., Bourbaki) refer to PIDs as principal rings. The distinction is that a principal ideal ring may have zero divisors whereas a principal ideal domain cannot. Principal ideal domains appear in the following chain of class inclusions:
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Principal ideal domain
In mathematics, a principal ideal domain, or PID, is an integral domain in which every ideal is principal, i.e., can be generated by a single element. More generally, a principal ideal ring is a nonzero commutative ring whose ideals are principal, although some authors (e.g., Bourbaki) refer to PIDs as principal rings. The distinction is that a principal ideal ring may have zero divisors whereas a principal ideal domain cannot. Principal ideal domains appear in the following chain of class inclusions:
has abstract
Dziedzina ideałów głównych (PI ...... jest pierścieniem całkowitym.
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Een hoofdideaaldomein is in de ...... lden in een hoofdideaaldomein.
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Em álgebra abstracta, um domín ...... s o inverso não é verdadeiro).
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En principalidealdomän (förkor ...... ersk ring och en Dedekindring.
@sv
En ringa teorio, ĉefideala int ...... s esprimeblaj kiel ĉefidealoj.
@eo
En àlgebra abstracta, un anell ...... s ⊃ Anells euclidians ⊃ cossos
@ca
In algebra, un dominio ad idea ...... i domini ad ideali principali.
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In mathematics, a principal id ...... ⊃ algebraically closed fields
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Les anneaux principaux forment ...... fondamental de l'arithmétique.
@fr
Obor hlavních ideálů je v abst ...... dy jedná o okruh noetherovský.
@cs
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June 2020
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incomplete sentence
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Dziedzina ideałów głównych (PI ...... jest pierścieniem całkowitym.
@pl
Een hoofdideaaldomein is in de ...... lden in een hoofdideaaldomein.
@nl
Em álgebra abstracta, um domín ...... s o inverso não é verdadeiro).
@pt
En principalidealdomän (förkor ...... ersk ring och en Dedekindring.
@sv
En ringa teorio, ĉefideala int ...... s esprimeblaj kiel ĉefidealoj.
@eo
En àlgebra abstracta, un anell ...... vol cos és un anell principal.
@ca
In algebra, un dominio ad idea ...... raverso un'identità di Bézout.
@it
In mathematics, a principal id ...... ing chain of class inclusions:
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Les anneaux principaux forment ...... fondamental de l'arithmétique.
@fr
Obor hlavních ideálů je v abst ...... dy jedná o okruh noetherovský.
@cs
label
Anell principal
@ca
Anneau principal
@fr
Dominio ad ideali principali
@it
Dominio de ideales principales
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Domínio principal
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Dziedzina ideałów głównych
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Hauptidealring
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Hoofdideaaldomein
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Obor hlavních ideálů
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Principal ideal domain
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