Integral domain
type: Ontology
creation date: 2026-08-24T18:15:07+00:00
imports: http://semantic-mediawiki.org/swivt/1.0

Integral domain
type: Subject
type: Category:Properties of commutative unital rings
type: Category:Standard terminology
type: Category:Basic definitions in commutative algebra
type: Category:Polynomial-closed properties of commutative unital rings
type: Category:Subring-closed properties of commutative unital rings
page: https://commalg.subwiki.org/wiki/Integral_domain
wiki namespace: 0
wiki page content language: en
importance rank: 1
wiki page modification date: 2008-05-12T16:23:46Z
modification date#aux: 2454599.1831713
wiki page sort key: Integral domain

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type: Subject
master page: Integral domain
wiki namespace: 0
query depth: 1
query format: plainlist
query size: 3
query string: [[Fact about::Integral domain]] [[Category:Commutative unital ring property implications]]
wiki page sort key: Integral domain# QUERY47a2c0558e24058b9294eb57c0910263

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type: Subject
master page: Integral domain
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query string: [[Fact about::Integral domain]] [[Category:Commutative unital ring property non-implications]]
wiki page sort key: Integral domain# QUERY0a49d78457fcc7307e5c22269fb2dec9

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type: Subject
master page: Integral domain
wiki namespace: 0
query depth: 1
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query string: [[Fact about::Integral domain]] [[Category:Commutative unital ring metaproperty satisfactions]]
wiki page sort key: Integral domain# QUERY6386190e70c903c552fdff591563787a

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type: Subject
master page: Integral domain
wiki namespace: 0
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query string: [[Fact about::Integral domain]] [[Category:Commutative unital ring metaproperty dissatisfactions]]
wiki page sort key: Integral domain# QUERY7839ee4c6d65de8b0a5d92080b70cf26

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type: Subject
master page: Integral domain
wiki namespace: 0
query depth: 1
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query size: 3
query string: [[Fact about::Integral domain]] [[Category:Commutative unital ring property satisfactions]]
wiki page sort key: Integral domain# QUERY5f9cc8fe4156bb668ae3ab2cf955a00d

http://commalg.subwiki.org/wiki/Special:URIResolver/Integral_domain-23_QUERY320f4b24f4f554110db8c632e34116c5
type: Subject
master page: Integral domain
wiki namespace: 0
query depth: 1
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query string: [[Fact about::Integral domain]] [[Category:Commutative unital ring property dissatisfactions]]
wiki page sort key: Integral domain# QUERY320f4b24f4f554110db8c632e34116c5

Ring over which every monic polynomial has finitely many roots
type: Subject
page: https://commalg.subwiki.org/wiki/Ring_over_which_every_monic_polynomial_has_finitely_many_roots
wiki namespace: 0
wiki page content language: en
weaker than: Integral domain
wiki page sort key: Ring over which every monic polynomial has finitely many roots

Ring over which every nonzero polynomial has finitely many roots
type: Subject
page: https://commalg.subwiki.org/wiki/Ring_over_which_every_nonzero_polynomial_has_finitely_many_roots
wiki namespace: 0
wiki page content language: en
weaker than: Integral domain
wiki page sort key: Ring over which every nonzero polynomial has finitely many roots

Prime ideal
type: Subject
page: https://commalg.subwiki.org/wiki/Prime_ideal
wiki namespace: 0
wiki page content language: en
defining ingredient: Integral domain
wiki page sort key: Prime ideal

Prime element
type: Subject
page: https://commalg.subwiki.org/wiki/Prime_element
wiki namespace: 0
wiki page content language: en
defining ingredient: Integral domain
wiki page sort key: Prime element

Dedekind-Hasse norm implies principal ideal ring
type: Subject
page: https://commalg.subwiki.org/wiki/Dedekind-2DHasse_norm_implies_principal_ideal_ring
wiki namespace: 0
wiki page content language: en
fact about: Integral domain
wiki page sort key: Dedekind-Hasse norm implies principal ideal ring

Associate implies same orbit under multiplication by group of units in integral domain
type: Subject
page: https://commalg.subwiki.org/wiki/Associate_implies_same_orbit_under_multiplication_by_group_of_units_in_integral_domain
wiki namespace: 0
wiki page content language: en
fact about: Integral domain
wiki page sort key: Associate implies same orbit under multiplication by group of units in integral domain

Integral domain satisfying ACCP that is not a field has either infinitely many units or infinitely many associate classes of irreducibles
type: Subject
page: https://commalg.subwiki.org/wiki/Integral_domain_satisfying_ACCP_that_is_not_a_field_has_either_infinitely_many_units_or_infinitely_many_associate_classes_of_irreducibles
wiki namespace: 0
wiki page content language: en
fact about: Integral domain
wiki page sort key: Integral domain satisfying ACCP that is not a field has either infinitely many units or infinitely many associate classes of irreducibles

Domain
type: Subject
page: https://commalg.subwiki.org/wiki/Domain
wiki namespace: 0
wiki page content language: en
redirects to: Integral domain
wiki page sort key: Domain

Weaker than
type: ObjectProperty
page: https://commalg.subwiki.org/wiki/Property-3AWeaker_than
wiki namespace: 132
wiki page content language: en
wiki page sort key: Weaker than

Defining ingredient
type: ObjectProperty
page: https://commalg.subwiki.org/wiki/Property-3ADefining_ingredient
wiki namespace: 132
wiki page content language: en
wiki page sort key: Defining ingredient

Fact about
type: ObjectProperty
page: https://commalg.subwiki.org/wiki/Property-3AFact_about
wiki namespace: 132
wiki page content language: en
wiki page sort key: Fact about

REDI
type: DatatypeProperty
page: https://commalg.subwiki.org/wiki/Property-3A_REDI
wiki namespace: 132
wiki page content language: en
wiki page sort key: REDI