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- GCD_domain abstract "In mathematics, a GCD domain is an integral domain R with the property that any two non-zero elements have a greatest common divisor (GCD). Equivalently, any two non-zero elements of R have a least common multiple (LCM).A GCD domain generalizes a unique factorization domain to the non-Noetherian setting in the following sense: an integral domain is a UFD if and only if it is a GCD domain satisfying the ascending chain condition on principal ideals (and in particular if it is Noetherian).GCD domains appear in the following chain of class inclusions: commutative rings ⊃ integral domains ⊃ integrally closed domains ⊃ GCD domains ⊃ unique factorization domains ⊃ principal ideal domains ⊃ Euclidean domains ⊃ fields ⊃ finite fields↑".
- GCD_domain wikiPageID "2932361".
- GCD_domain wikiPageLength "4355".
- GCD_domain wikiPageOutDegree "24".
- GCD_domain wikiPageRevisionID "700840422".
- GCD_domain wikiPageWikiLink Ascending_chain_condition_on_principal_ideals.
- GCD_domain wikiPageWikiLink Atomic_domain.
- GCD_domain wikiPageWikiLink Bézout_domain.
- GCD_domain wikiPageWikiLink Category:Commutative_algebra.
- GCD_domain wikiPageWikiLink Category:Ring_theory.
- GCD_domain wikiPageWikiLink Complete_lattice.
- GCD_domain wikiPageWikiLink Distributive_lattice.
- GCD_domain wikiPageWikiLink Entire_function.
- GCD_domain wikiPageWikiLink Gausss_lemma_(polynomial).
- GCD_domain wikiPageWikiLink Greatest_common_divisor.
- GCD_domain wikiPageWikiLink Integral_domain.
- GCD_domain wikiPageWikiLink Integrally_closed.
- GCD_domain wikiPageWikiLink Least_common_multiple.
- GCD_domain wikiPageWikiLink Noetherian.
- GCD_domain wikiPageWikiLink Principal_ideal_domain.
- GCD_domain wikiPageWikiLink Prüfer_domain.
- GCD_domain wikiPageWikiLink Schreier_domain.
- GCD_domain wikiPageWikiLink Subclass_(set_theory).
- GCD_domain wikiPageWikiLink Unique_factorization_domain.
- GCD_domain wikiPageWikiLinkText "GCD domain".
- GCD_domain wikiPageUsesTemplate Template:=.
- GCD_domain wikiPageUsesTemplate Template:Citation_needed.
- GCD_domain wikiPageUsesTemplate Template:Commutative_ring_classes.
- GCD_domain subject Category:Commutative_algebra.
- GCD_domain subject Category:Ring_theory.
- GCD_domain hypernym R.
- GCD_domain type Redirect.
- GCD_domain comment "In mathematics, a GCD domain is an integral domain R with the property that any two non-zero elements have a greatest common divisor (GCD).".
- GCD_domain label "GCD domain".
- GCD_domain sameAs Q2851438.
- GCD_domain sameAs Anneau_à_PGCD.
- GCD_domain sameAs GCD整域.
- GCD_domain sameAs m.08dhsq.
- GCD_domain sameAs Q2851438.
- GCD_domain sameAs GCD環.
- GCD_domain wasDerivedFrom GCD_domain?oldid=700840422.
- GCD_domain isPrimaryTopicOf GCD_domain.