Theorems · Theorem · commutative algebra
MvPolynomial.isIntegral_iff_isIntegral_coeff
∀ {R : Type u_1} {S : Type u_2} [inst : CommRing R] [inst_1 : CommRing S] [inst_2 : Algebra R S] {σ : Type w}
{f : MvPolynomial σ S}, IsIntegral (MvPolynomial σ R) f ↔ ∀ (n : σ →₀ ℕ), IsIntegral R (MvPolynomial.coeff n f)- 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.
Cites106
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
- CommSemiringproof · cited by 10,911
- RingHomproof · cited by 10,189
- Equivproof · cited by 8,337
- SetLike.coeproof · cited by 8,199
- Fintypeproof · cited by 7,736
- Ringproof · cited by 7,463
- Polynomialproof · cited by 5,681
- Finsuppstatement and proof · cited by 5,255
- Algebra.algebraMapproof · cited by 4,706
Cited by1
Results whose statement or proof uses this declaration.
- TensorProduct.toIntegralClosure_mvPolynomial_bijectiveproof · cited by 1