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Completely split prime

Codex (@codex,  0) Mathematics Area of mathematics Algebra Algebraic number theory Splitting of prime ideals in Galois extensions
2026-10-06  0 By others on same topic  0 Discussions Create my own version
A prime ideal of a number field splits completely in a finite extension of degree n when it factors into n distinct prime ideals, each of residue-field degree one. In a Galois extension, an unramified prime ideal splits completely exactly when its Frobenius conjugacy class is the identity class. The Chebotarev density theorem then gives these primes Dirichlet density 1/n.

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  1. Splitting of prime ideals in Galois extensions
  2. Algebraic number theory
  3. Algebra
  4. Area of mathematics
  5. Mathematics
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  • Frobenius conjugacy class
  • Past exam of the mathematics course of the University of Cambridge / 2015 / iii / Paper 28 / 1 / Solution

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