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- Atomic_domain abstract "In mathematics, more specifically ring theory, an atomic domain or factorization domain is an integral domain, every non-zero non-unit of which can be written (in at least one way) as a (finite) product of irreducible elements. Atomic domains are different from unique factorization domains in that this decomposition of an element into irreducibles need not be unique; stated differently, an irreducible element is not necessarily a prime element. Important examples of atomic domains include the class of all unique factorization domains and all Noetherian domains. More generally, any integral domain satisfying the ascending chain condition on principal ideals (i.e. the ACCP), is an atomic domain. Although the converse is claimed to hold in Cohn's paper, this is known to be false.The term \"atomic\" is due to P. M. Cohn, who called an irreducible element of an integral domain an \"atom\".".
- Atomic_domain wikiPageExternalLink bezout_rings_and_their_subrings.pdf.
- Atomic_domain wikiPageID "9599592".
- Atomic_domain wikiPageLength "4941".
- Atomic_domain wikiPageOutDegree "22".
- Atomic_domain wikiPageRevisionID "615262920".
- Atomic_domain wikiPageWikiLink Ascending_chain_condition_on_principal_ideals.
- Atomic_domain wikiPageWikiLink Category:Commutative_algebra.
- Atomic_domain wikiPageWikiLink Fundamental_theorem_of_arithmetic.
- Atomic_domain wikiPageWikiLink Infinite_product.
- Atomic_domain wikiPageWikiLink Integral_domain.
- Atomic_domain wikiPageWikiLink Irreducible_element.
- Atomic_domain wikiPageWikiLink Mathematics.
- Atomic_domain wikiPageWikiLink Noetherian_ring.
- Atomic_domain wikiPageWikiLink Paul_Cohn.
- Atomic_domain wikiPageWikiLink Prime_element.
- Atomic_domain wikiPageWikiLink Prime_number.
- Atomic_domain wikiPageWikiLink Ring_theory.
- Atomic_domain wikiPageWikiLink Unique_factorization_domain.
- Atomic_domain wikiPageWikiLink Unit_(ring_theory).
- Atomic_domain wikiPageWikiLinkText "Atomic domain".
- Atomic_domain wikiPageWikiLinkText "atomic domain".
- Atomic_domain wikiPageWikiLinkText "atomic".
- Atomic_domain wikiPageUsesTemplate Template:=.
- Atomic_domain wikiPageUsesTemplate Template:Reflist.
- Atomic_domain subject Category:Commutative_algebra.
- Atomic_domain hypernym Domain.
- Atomic_domain type Protein.
- Atomic_domain comment "In mathematics, more specifically ring theory, an atomic domain or factorization domain is an integral domain, every non-zero non-unit of which can be written (in at least one way) as a (finite) product of irreducible elements. Atomic domains are different from unique factorization domains in that this decomposition of an element into irreducibles need not be unique; stated differently, an irreducible element is not necessarily a prime element.".
- Atomic_domain label "Atomic domain".
- Atomic_domain sameAs Q257414.
- Atomic_domain sameAs תחום_אטומי.
- Atomic_domain sameAs m.05q9jxq.
- Atomic_domain sameAs Q257414.
- Atomic_domain wasDerivedFrom Atomic_domain?oldid=615262920.
- Atomic_domain isPrimaryTopicOf Atomic_domain.