Theorems · Theorem · commutative algebra
MvPolynomial.isUnit_iff
∀ {σ : Type u_1} {R : Type u_2} [inst : CommRing R] {P : MvPolynomial σ R},
IsUnit P ↔ IsUnit (MvPolynomial.coeff 0 P) ∧ ∀ (i : σ →₀ ℕ), i ≠ 0 → IsNilpotent (MvPolynomial.coeff i P)- Defined in
- Mathlib.Algebra.MvPolynomial.Nilpotent
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 121 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- CommRing
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites38
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
- CommSemiringproof · cited by 10,911
- Polynomialproof · cited by 5,681
- Finsuppstatement and proof · cited by 5,255
- Equiv.symmproof · cited by 3,681
- MvPolynomialstatement and proof · cited by 2,140
- AlgEquivproof · cited by 1,681
- IsUnitstatement and proof · cited by 1,602
- Polynomial.coeffproof · cited by 1,045
- sub_selfproof · cited by 996
- sub_zeroproof · cited by 938
Cited by2
Results whose statement or proof uses this declaration.
- MvPolynomial.isUnit_iff_totalDegree_of_isReducedproof · cited by 3
- MvPolynomial.isLocalHom_expandproof · cited by 1