Theorems · Theorem · commutative algebra
IsIntegral.pow
∀ {R : Type u_1} {B : Type u_3} [inst : CommRing R] [inst_1 : Ring B] [inst_2 : Algebra R B] {x : B},
IsIntegral R x → ∀ (n : ℕ), IsIntegral R (x ^ n)- Cited by
- 12 results in Mathlib
- Foundations
- Depth 132 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites9
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
- Ringstatement and proof · cited by 7,463
- Algebra.adjoinproof · cited by 535
- IsIntegralstatement and proof · cited by 427
- Algebra.subset_adjoinproof · cited by 109
- Subalgebra.pow_memproof · cited by 19
- IsIntegral.of_mem_of_fgproof · cited by 13
- IsIntegral.fg_adjoin_singletonproof · cited by 13
Cited by12
Results whose statement or proof uses this declaration.
- Algebra.isIntegral_normproof · cited by 4
- NumberField.Embeddings.pow_eq_one_of_norm_le_oneproof · cited by 2
- dvd_coeff_zero_of_aeval_eq_prime_smul_of_minpoly_isEisensteinAtproof · cited by 1
- IsIntegral.pow_iffproof · cited by 1
- Polynomial.isIntegral_iff_isIntegral_coeffproof · cited by 1
- Algebra.discr_mul_isIntegral_mem_adjoinproof · cited by 1
- mem_adjoin_of_smul_prime_smul_of_minpoly_isEisensteinAtproof · cited by 1
- MvPolynomial.isIntegral_iff_isIntegral_coeffproof · cited by 1
- minpoly.iterateFrobenius_of_isSeparableproof · cited by 1
- Algebra.dvd_algebraMap_intNorm_selfproof · cited by 1
- Algebra.ZariskisMainProperty.transproof · cited by 0
- IsLocalization.Away.exists_isIntegral_mul_of_isIntegral_mk'proof · cited by 0