Theorems · Theorem · commutative algebra
IsIntegral.of_pow
∀ {R : Type u_1} {B : Type u_3} [inst : CommRing R] [inst_1 : Ring B] [inst_2 : Algebra R B] {x : B} {n : ℕ},
0 < n → IsIntegral R (x ^ n) → IsIntegral R x- Cited by
- 4 results in Mathlib
- Foundations
- Depth 116 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites13
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- CommRingstatement and proof · cited by 17,173
- Algebrastatement and proof · cited by 11,388
- Ringstatement and proof · cited by 7,463
- Polynomialproof · cited by 5,681
- Algebra.algebraMapproof · cited by 4,706
- Polynomial.Monicproof · cited by 461
- IsIntegralstatement and proof · cited by 427
- Polynomial.eval₂proof · cited by 267
- Polynomial.expandproof · cited by 90
- Polynomial.aeval_defproof · cited by 51
- Polynomial.expand_aevalproof · cited by 4
Cited by4
Results whose statement or proof uses this declaration.
- Complex.isIntegral_exp_rat_mul_pi_mul_Iproof · cited by 3
- IsIntegrallyClosedIn.exists_algebraMap_eq_of_isIntegral_powproof · cited by 2
- IsIntegral.pow_iffproof · cited by 1
- PrimeSpectrum.isHomeomorph_comapproof · cited by 1