Let be a non-Archimedean valuated field. Its valuation ring is defined to be

The valuation ring has maximal Ideal

and the field is called the residue field, class field, or field of digits. For example, if (-adic numbers), then (-adic integers), (-adic integers congruent to 0 mod ), and = GF(), the Finite Field of order .

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1999-05-26