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- Q986694 subject Q8399470.
- Q986694 subject Q8600954.
- Q986694 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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- Q986694 wikiPageWikiLink Q8399470.
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- Q986694 wikiPageWikiLink Q8600954.
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- Q986694 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.".
- Q986694 label "Discrete valuation ring".