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- Integral_domain abstract "In mathematics, and specifically in abstract algebra, an integral domain is a nonzero commutative ring in which the product of any two nonzero elements is nonzero. Integral domains are generalizations of the ring of integers and provide a natural setting for studying divisibility."Integral domain" is defined almost universally as above, but there is some variation. This article follows the convention that rings have a 1, but some authors who do not follow this also do not require integral domains to have a 1. Noncommutative integral domains are sometimes admitted. This article, however, follows the much more usual convention of reserving the term "integral domain" for the commutative case and using "domain" for the general case including noncommutative rings.Some sources, notably Lang, use the term entire ring for integral domain.Some specific kinds of integral domains are given with the following chain of class inclusions: Commutative rings ⊃ integral domains ⊃ integrally closed domains ⊃ unique factorization domains ⊃ principal ideal domains ⊃ Euclidean domains ⊃ fieldsThe absence of nonzero zero divisors implies that in an integral domain the cancellation property holds for multiplication by any nonzero element a: an equality ab = ac implies b = c.".
- Integral_domain wikiPageID "15462".
- Integral_domain wikiPageRevisionID "605113188".
- Integral_domain hasPhotoCollection Integral_domain.
- Integral_domain subject Category:Commutative_algebra.
- Integral_domain subject Category:Ring_theory.
- Integral_domain comment "In mathematics, and specifically in abstract algebra, an integral domain is a nonzero commutative ring in which the product of any two nonzero elements is nonzero. Integral domains are generalizations of the ring of integers and provide a natural setting for studying divisibility."Integral domain" is defined almost universally as above, but there is some variation.".
- Integral_domain label "Anneau intègre".
- Integral_domain label "Dominio d'integrità".
- Integral_domain label "Dominio de integridad".
- Integral_domain label "Domínio de integridade".
- Integral_domain label "Dziedzina całkowitości".
- Integral_domain label "Integral domain".
- Integral_domain label "Integriteitsdomein".
- Integral_domain label "Integritätsring".
- Integral_domain label "Область целостности".
- Integral_domain label "整域".
- Integral_domain label "整环".
- Integral_domain sameAs Obor_integrity.
- Integral_domain sameAs Integritätsring.
- Integral_domain sameAs Ακέραια_περιοχή.
- Integral_domain sameAs Dominio_de_integridad.
- Integral_domain sameAs Anneau_intègre.
- Integral_domain sameAs Dominio_d'integrità.
- Integral_domain sameAs 整域.
- Integral_domain sameAs 정역.
- Integral_domain sameAs Integriteitsdomein.
- Integral_domain sameAs Dziedzina_całkowitości.
- Integral_domain sameAs Domínio_de_integridade.
- Integral_domain sameAs m.03zm6.
- Integral_domain sameAs Q628792.
- Integral_domain sameAs Q628792.
- Integral_domain wasDerivedFrom Integral_domain?oldid=605113188.
- Integral_domain isPrimaryTopicOf Integral_domain.