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Any nonzero commutative ring in which the product of nonzero elements is nonzero.
Definition source: English Wiktionary via Wiktextract
Qualifier: ring theory
Topics: algebra, mathematics, sciences
Examples
- A ring R is an integral domain if and only if the polynomial ring R#91;x#93; is an integral domain.
- For any integral domain there can be derived an associated field of fractions.
Meaning relationships
Synonyms: none provided
Antonyms: none provided
No etymology was provided for this word.
Across languages
Translations
11 source translations are retained for this English entry.
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Finnish:
kokonaisalue
— nonzero commutative ring in which the product of nonzero elements is nonzero
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French:
anneau d'intégrité
— nonzero commutative ring in which the product of nonzero elements is nonzero
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Italian:
dominio d'integrità
— nonzero commutative ring in which the product of nonzero elements is nonzero
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Polish:
dziedzina całkowitości
— nonzero commutative ring in which the product of nonzero elements is nonzero
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Serbo-Croatian:
област цијелих
— nonzero commutative ring in which the product of nonzero elements is nonzero
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Serbo-Croatian:
област целих
— nonzero commutative ring in which the product of nonzero elements is nonzero
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Serbo-Croatian:
домен
— nonzero commutative ring in which the product of nonzero elements is nonzero
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Serbo-Croatian:
oblast cijelih
— nonzero commutative ring in which the product of nonzero elements is nonzero
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Serbo-Croatian:
oblast celih
— nonzero commutative ring in which the product of nonzero elements is nonzero
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Serbo-Croatian:
domen
— nonzero commutative ring in which the product of nonzero elements is nonzero
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Spanish:
dominio de integridad
— nonzero commutative ring in which the product of nonzero elements is nonzero
