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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}.".
- Discrete_valuation_ring wikiPageExternalLink d033180.htm.
- Discrete_valuation_ring wikiPageID "848633".
- Discrete_valuation_ring wikiPageRevisionID "563114756".
- Discrete_valuation_ring hasPhotoCollection Discrete_valuation_ring.
- Discrete_valuation_ring subject Category:Commutative_algebra.
- Discrete_valuation_ring subject Category:Localization_(mathematics).
- 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 "Anello a valutazione discreta".
- Discrete_valuation_ring label "Anneau de valuation discrète".
- Discrete_valuation_ring label "Discrete valuation ring".
- Discrete_valuation_ring label "Diskreter Bewertungsring".
- Discrete_valuation_ring label "Кольцо дискретного нормирования".
- Discrete_valuation_ring sameAs Diskreter_Bewertungsring.
- Discrete_valuation_ring sameAs Anneau_de_valuation_discrète.
- Discrete_valuation_ring sameAs Anello_a_valutazione_discreta.
- Discrete_valuation_ring sameAs m.03gvvp.
- Discrete_valuation_ring sameAs Q986694.
- Discrete_valuation_ring sameAs Q986694.
- Discrete_valuation_ring wasDerivedFrom Discrete_valuation_ring?oldid=563114756.
- Discrete_valuation_ring isPrimaryTopicOf Discrete_valuation_ring.