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An integral domain in which every proper ideal factors into a product of prime ideals which is unique (up to permutations).
Definition source: English Wiktionary via Wiktextract
Qualifier: ring theory
Topics: algebra, mathematics, sciences
Examples
- It can be proved that a Dedekind domain (as defined above) is equivalent to an integral domain in which every proper fractional ideal is invertible.
Meaning relationships
Synonyms: none provided
Antonyms: none provided
Named after German mathematician Richard Dedekind (1831–1916).
Across languages
Translations
7 source translations are retained for this English entry.
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French:
anneau de Dedekind
— integral domain whose prime ideals factorise uniquely
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German:
Dedekindring
— integral domain whose prime ideals factorise uniquely
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Italian:
dominio di Dedekind
— integral domain whose prime ideals factorise uniquely
-
Italian:
anello di Dedekind
— integral domain whose prime ideals factorise uniquely
-
Polish:
pierścień Dedekinda
— integral domain whose prime ideals factorise uniquely
-
Portuguese:
domínio de Dedekind
— integral domain whose prime ideals factorise uniquely
-
Portuguese:
anel de Dedekind
— integral domain whose prime ideals factorise uniquely
