Theorems · Theorem · number theory
IsCyclotomicExtension.integral
∀ (S : Set ℕ) (A : Type u) (B : Type v) [inst : CommRing A] [inst_1 : CommRing B] [inst_2 : Algebra A B] [IsCyclotomicExtension S A B], Algebra.IsIntegral A B
A cyclotomic extension is integral.
- Defined in
- Mathlib.NumberTheory.Cyclotomic.Basic
- Cited by
- 2 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.
Cites22
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
- Top.topproof · cited by 9,680
- Set.ofPredproof · cited by 6,101
- Algebra.algebraMapproof · cited by 4,706
- Polynomial.Xproof · cited by 1,639
- sub_selfproof · cited by 996
- Algebra.adjoinproof · cited by 535
- IsIntegralproof · cited by 427
- Algebra.IsIntegralstatement · cited by 224
- IsCyclotomicExtensionstatement and proof · cited by 220
Cited by2
Results whose statement or proof uses this declaration.
- IsCyclotomicExtension.isSeparableproof · cited by 3
- IsCyclotomicExtension.Rat.isCMFieldproof · cited by 0