Theorems · Theorem · commutative algebra
IsIntegral.coeff
∀ {R : Type u_1} {S : Type u_2} [inst : CommRing R] [inst_1 : CommRing S] [inst_2 : Algebra R S] {p : Polynomial S},
IsIntegral (Polynomial R) p → ∀ (i : ℕ), IsIntegral R (p.coeff i)[Stacks Tag 00H0](https://stacks.math.columbia.edu/tag/00H0) ((2))
- Defined in
- Mathlib.RingTheory.Polynomial.IsIntegral
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 140 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites66
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
- Polynomialstatement and proof · cited by 5,681
- Algebra.algebraMapproof · cited by 4,706
- one_mulproof · cited by 2,841
- Nontrivialproof · cited by 2,416
- le_reflproof · cited by 2,061
- Polynomial.Xproof · cited by 1,639
- Finset.rangeproof · cited by 1,341
- eq_or_neproof · cited by 1,117
- Polynomial.natDegreeproof · cited by 1,105
Cited by4
Results whose statement or proof uses this declaration.
- MvPolynomial.isIntegral_iff_isIntegral_coeffproof · cited by 1
- Polynomial.isIntegral_iff_isIntegral_coeffproof · cited by 1
- IsIntegral.coeff_of_exists_smul_mem_liftsproof · cited by 0
- IsIntegral.coeff_of_isFractionRingproof · cited by 0