Theorems · Theorem · commutative algebra
Polynomial.isIntegral_iff_isIntegral_coeff
∀ {R : Type u_1} {S : Type u_2} [inst : CommRing R] [inst_1 : CommRing S] [inst_2 : Algebra R S] {f : Polynomial S},
IsIntegral (Polynomial R) f ↔ ∀ (n : ℕ), IsIntegral R (f.coeff n)- Defined in
- Mathlib.RingTheory.Polynomial.IsIntegral
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 141 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites24
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
- Finset.sum_congrproof · cited by 2,323
- Polynomial.Xproof · cited by 1,639
- Polynomial.Cproof · cited by 1,598
- Polynomial.coeffstatement and proof · cited by 1,045
- Polynomial.mapproof · cited by 806
- IsIntegralstatement and proof · cited by 427
- Polynomial.monomialproof · cited by 256
Cited by1
Results whose statement or proof uses this declaration.
- exists_derivative_mul_eq_and_isIntegral_coeffproof · cited by 1