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Valuation ring

In abstract algebra, a valuation ring is an integral domainD such that for every non-zero element x of its field of fractionsF, at least one of x or x belongs to D. Given a fieldF, if D is a subring of F such that either x or x belongs to D for every nonzero x in F, then D is said to be a valuation ring for the field F or a place of F. Since F in this case is indeed the field of fractions of D, a valuation ring for a field is a valuation ring.

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