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- Discrete_valuation_ring abstract "In abstract algebra, a discrete valuation ring (DVR) is a principal ideal domain (PID) with exactly one non-zero maximal ideal.This means a DVR is an integral domain R which satisfies any one of the following equivalent conditions: R is a local principal ideal domain, and not a field. R is a valuation ring with a value group isomorphic to the integers under addition. R is a local Dedekind domain and not a field. R is a Noetherian local ring with Krull dimension one, and the maximal ideal of R is principal. R is an integrally closed Noetherian local ring with Krull dimension one. R is a principal ideal domain with a unique non-zero prime ideal. R is a principal ideal domain with a unique irreducible element (up to multiplication by units). R is a unique factorization domain with a unique irreducible element (up to multiplication by units). R is not a field, and every nonzero fractional ideal of R is irreducible in the sense that it cannot be written as finite intersection of fractional ideals properly containing it. There is some discrete valuation ν on the field of fractions K of R, such that R={x : x in K, ν(x) ≥ 0}.".
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- Discrete_valuation_ring wikiPageRevisionID "668632590".
- Discrete_valuation_ring wikiPageWikiLink Absolute_value_(algebra).
- Discrete_valuation_ring wikiPageWikiLink Abstract_algebra.
- Discrete_valuation_ring wikiPageWikiLink Category:Commutative_algebra.
- Discrete_valuation_ring wikiPageWikiLink Category:Localization_(mathematics).
- Discrete_valuation_ring wikiPageWikiLink Cohen_ring.
- Discrete_valuation_ring wikiPageWikiLink Compact_space.
- Discrete_valuation_ring wikiPageWikiLink Complete_metric_space.
- Discrete_valuation_ring wikiPageWikiLink Complete_space.
- Discrete_valuation_ring wikiPageWikiLink Complex_number.
- Discrete_valuation_ring wikiPageWikiLink Dedekind_domain.
- Discrete_valuation_ring wikiPageWikiLink Discrete_valuation.
- Discrete_valuation_ring wikiPageWikiLink Encyclopaedia_of_Mathematics.
- Discrete_valuation_ring wikiPageWikiLink Encyclopedia_of_Mathematics.
- Discrete_valuation_ring wikiPageWikiLink Euclidean_domain.
- Discrete_valuation_ring wikiPageWikiLink Field_(mathematics).
- Discrete_valuation_ring wikiPageWikiLink Field_of_fractions.
- Discrete_valuation_ring wikiPageWikiLink Finite_field.
- Discrete_valuation_ring wikiPageWikiLink Formal_power_series.
- Discrete_valuation_ring wikiPageWikiLink Fractional_ideal.
- Discrete_valuation_ring wikiPageWikiLink Fundamental_theorem_of_arithmetic.
- Discrete_valuation_ring wikiPageWikiLink Ideal_(ring_theory).
- Discrete_valuation_ring wikiPageWikiLink If_and_only_if.
- Discrete_valuation_ring wikiPageWikiLink Iff.
- Discrete_valuation_ring wikiPageWikiLink Integral_domain.
- Discrete_valuation_ring wikiPageWikiLink Integrally_closed.
- Discrete_valuation_ring wikiPageWikiLink Irreducible_element.
- Discrete_valuation_ring wikiPageWikiLink Irreducible_ideal.
- Discrete_valuation_ring wikiPageWikiLink John_Wiley_&_Sons.
- Discrete_valuation_ring wikiPageWikiLink Krull_dimension.
- Discrete_valuation_ring wikiPageWikiLink Local_ring.
- Discrete_valuation_ring wikiPageWikiLink Localization_of_a_ring.
- Discrete_valuation_ring wikiPageWikiLink Maximal_ideal.
- Discrete_valuation_ring wikiPageWikiLink Neighborhood_(topology).
- Discrete_valuation_ring wikiPageWikiLink Neighbourhood_(mathematics).
- Discrete_valuation_ring wikiPageWikiLink Noetherian.
- Discrete_valuation_ring wikiPageWikiLink P-adic_integer.
- Discrete_valuation_ring wikiPageWikiLink P-adic_number.
- Discrete_valuation_ring wikiPageWikiLink Polynomial.
- Discrete_valuation_ring wikiPageWikiLink Prime_ideal.
- Discrete_valuation_ring wikiPageWikiLink Prime_number.
- Discrete_valuation_ring wikiPageWikiLink Principal_ideal_domain.
- Discrete_valuation_ring wikiPageWikiLink Rational_function.
- Discrete_valuation_ring wikiPageWikiLink Real_number.
- Discrete_valuation_ring wikiPageWikiLink Residue_field.
- Discrete_valuation_ring wikiPageWikiLink Subring.
- Discrete_valuation_ring wikiPageWikiLink T.
- Discrete_valuation_ring wikiPageWikiLink Topological_ring.
- Discrete_valuation_ring wikiPageWikiLink Unique_factorization_domain.
- Discrete_valuation_ring wikiPageWikiLink Unit_(ring_theory).
- Discrete_valuation_ring wikiPageWikiLink Up_to.
- Discrete_valuation_ring wikiPageWikiLink Valuation_ring.
- Discrete_valuation_ring wikiPageWikiLinkText "DVR".
- Discrete_valuation_ring wikiPageWikiLinkText "Discrete valuation ring".
- Discrete_valuation_ring wikiPageWikiLinkText "Discrete valuation ring#Topology".
- Discrete_valuation_ring wikiPageWikiLinkText "Discrete valuation ring#uniformizer".
- Discrete_valuation_ring wikiPageWikiLinkText "Discrete_valuation_ring#Uniformizing_parameter".
- Discrete_valuation_ring wikiPageWikiLinkText "discrete valuation ring".
- Discrete_valuation_ring wikiPageWikiLinkText "prime element".
- Discrete_valuation_ring wikiPageWikiLinkText "uniformizing parameter".
- Discrete_valuation_ring hasPhotoCollection Discrete_valuation_ring.
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- Discrete_valuation_ring wikiPageUsesTemplate Template:Citation_needed.
- Discrete_valuation_ring wikiPageUsesTemplate Template:No_footnotes.
- Discrete_valuation_ring subject Category:Commutative_algebra.
- Discrete_valuation_ring subject Category:Localization_(mathematics).
- Discrete_valuation_ring hypernym Domain.
- Discrete_valuation_ring type Protein.
- Discrete_valuation_ring comment "In abstract algebra, a discrete valuation ring (DVR) is a principal ideal domain (PID) with exactly one non-zero maximal ideal.This means a DVR is an integral domain R which satisfies any one of the following equivalent conditions: R is a local principal ideal domain, and not a field. R is a valuation ring with a value group isomorphic to the integers under addition. R is a local Dedekind domain and not a field.".
- Discrete_valuation_ring label "Discrete valuation ring".
- Discrete_valuation_ring sameAs Diskreter_Bewertungsring.
- Discrete_valuation_ring sameAs Anneau_de_valuation_discrète.
- Discrete_valuation_ring sameAs תחום_הערכה_דיסקרטית.
- Discrete_valuation_ring sameAs Anello_a_valutazione_discreta.
- Discrete_valuation_ring sameAs 離散付値環.
- Discrete_valuation_ring sameAs 이산_값매김환.
- Discrete_valuation_ring sameAs m.03gvvp.
- Discrete_valuation_ring sameAs Кольцо_дискретного_нормирования.
- Discrete_valuation_ring sameAs Q986694.
- Discrete_valuation_ring sameAs Q986694.
- Discrete_valuation_ring wasDerivedFrom Discrete_valuation_ring?oldid=668632590.
- Discrete_valuation_ring isPrimaryTopicOf Discrete_valuation_ring.