p-adic number field

← Encyclopedia

External reading guide · Graduate

Completing the rationals for the p-adic absolute value produces a field with nonarchimedean convergence. Compute digit expansions before studying its valuation ring and local-field extensions.

Before opening the references

p-adic additive valuation · Cauchy sequence · field

Where to read

  1. Start here: Algebraic Number Theory (v3.08)

    James S. Milne · Lecture notes · English · Free full text

    Chapter 7 Absolute Values; Local Fields, Completions, Remark 7.24, Proposition 7.26 (valuation expansions), and Examples 7.27–7.29

    Source page · Checked 2026-10-16

Continue from here

Algebraic Number Theory & Class Field Theory in the library · Preparation and skip guidance · Terminology and translation evidence

Suggest an edit · Report a correction

Original orientation: CC BY-SA 4.0. Linked texts retain their own licences.