Theorems · Theorem · number theory
CyclotomicRing.eq_adjoin_primitive_root
∀ (n : ℕ) [NeZero n] (A : Type u) (K : Type w) [inst : CommRing A] [inst_1 : Field K] [inst_2 : Algebra A K]
{μ : CyclotomicField n K}, IsPrimitiveRoot μ n → CyclotomicRing n A K = ↥A[μ]- Defined in
- Mathlib.NumberTheory.Cyclotomic.Basic
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 214 from the axioms · uses propext, Classical.choice, Quot.sound
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Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement · 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.ofPredproof · cited by 6,101
- Subalgebrastatement and proof · cited by 1,353
- Algebra.adjoinstatement and proof · cited by 535
- IsPrimitiveRootstatement and proof · cited by 356
- CyclotomicFieldstatement and proof · cited by 14
- CyclotomicRingstatement and proof · cited by 6
- IsCyclotomicExtension.adjoin_roots_cyclotomic_eq_adjoin_nth_rootsproof · cited by 3
- IsCyclotomicExtension.adjoin_roots_cyclotomic_eq_adjoin_root_cyclotomicproof · cited by 2
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