Hensel's lemma

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A simple root over the residue field lifts to a root in a complete discrete valuation ring. Follow Newton's successive corrections, then compare the coprime-factor lifting form of Hensel's lemma.

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p-adic number field · polynomial ring · Integer Congruence

Where to read

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

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

    Chapter 7, Newton's lemma, Proposition 7.31 (simple-root lifting), and Theorem 7.33 (Hensel's lemma, coprime-factor lifting), printed pp. 120–121

    Source page · Checked 2026-10-16

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