Valuation Ring - Units and Maximal Ideals

Units and Maximal Ideals

The units, or invertible elements, of a valuation ring are the elements x such that x −1 is also a member of D. The other elements of D, called nonunits, do not have an inverse, and they form an ideal M. This ideal is maximal among the (totally ordered) ideals of D. Since M is a maximal ideal, the quotient ring D/M is a field, called the residue field of D.

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