Theorems · Theorem · number theory
NumberField.finrank_eq_one_of_unramified
∀ {K : Type u_1} {𝒪 : Type u_2} [inst : Field K] [inst_1 : NumberField K] [inst_2 : CommRing 𝒪] [inst_3 : Algebra 𝒪 K]
[IsIntegralClosure 𝒪 ℤ K] [Algebra.Unramified ℤ 𝒪], Module.finrank ℚ K = 1Any number field that is unramified over ℚ has rank 1.
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 319 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites11
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- CommRingstatement and proof · cited by 17,173
- Algebrastatement and proof · cited by 11,388
- Fieldstatement and proof · cited by 7,404
- Idealproof · cited by 4,748
- Module.finrankstatement and proof · cited by 1,770
- NumberFieldstatement and proof · cited by 653
- Ideal.IsMaximalproof · cited by 452
- IsIntegralClosurestatement and proof · cited by 146
- Algebra.IsUnramifiedAtproof · cited by 35
- Algebra.Unramifiedstatement and proof · cited by 10
- NumberField.exists_not_isUnramifiedAt_intproof · cited by 2
Cited by1
Results whose statement or proof uses this declaration.
- bijective_algebraMap_int_of_finite_of_unramifiedproof · cited by 0