A prime ramifies in a number field when its prime-ideal factorization contains a factor with exponent greater than one.
A finite extension of number fields is unramified everywhere when every finite prime ideal is unramified. If infinite places are included in the convention, one also requires every real place to remain real.

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  1. Splitting of rational primes in a quadratic field
  2. Splitting of prime ideals in Galois extensions
  3. Algebraic number theory
  4. Algebra
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