Theorems · Theorem · number theory
IsCyclotomicExtension.finiteDimensional
∀ (S : Set ℕ) (K : Type w) [inst : Field K] (C : Type z) [Finite ↑S] [inst_2 : CommRing C] [inst_3 : Algebra K C] [IsDomain C] [IsCyclotomicExtension S K C], FiniteDimensional K C
If S is finite and IsCyclotomicExtension S K A, then finiteDimensional K A.
- Defined in
- Mathlib.NumberTheory.Cyclotomic.Basic
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 138 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites10
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement and proof · cited by 53,352
- CommRingstatement and proof · cited by 17,173
- Algebrastatement and proof · cited by 11,388
- Fieldstatement and proof · cited by 7,404
- Set.Elemstatement and proof · cited by 7,166
- Finitestatement and proof · cited by 3,029
- IsDomainstatement and proof · cited by 2,196
- FiniteDimensionalstatement · cited by 1,854
- IsCyclotomicExtensionstatement and proof · cited by 220
- IsCyclotomicExtension.finiteproof · cited by 1
Cited by4
Results whose statement or proof uses this declaration.
- IsPrimitiveRoot.norm_pow_sub_one_of_prime_pow_ne_twoproof · cited by 4
- IsCyclotomicExtension.discr_prime_pow_ne_twoproof · cited by 4
- IsPrimitiveRoot.sub_one_norm_eq_eval_cyclotomicproof · cited by 3