Theorems · Theorem · commutative algebra
MvPolynomial.isNilpotent_iff
∀ {σ : Type u_1} {R : Type u_2} [inst : CommRing R] {P : MvPolynomial σ R},
IsNilpotent P ↔ ∀ (i : σ →₀ ℕ), IsNilpotent (MvPolynomial.coeff i P)- Defined in
- Mathlib.Algebra.MvPolynomial.Nilpotent
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 119 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- CommRing
Around this declaration
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Cites17
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
- Finsuppstatement and proof · cited by 5,255
- Set.rangeproof · cited by 4,705
- MvPolynomialstatement and proof · cited by 2,140
- Function.Embeddingproof · cited by 988
- MvPolynomial.coeffstatement and proof · cited by 315
- IsNilpotentstatement and proof · cited by 248
- Finsupp.mapDomainproof · cited by 168
- MvPolynomial.renameproof · cited by 168
- Finsupp.embDomainproof · cited by 69
- Finsupp.embDomain_eq_mapDomainproof · cited by 13
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