Theorems · Theorem · commutative algebra
MvPolynomial.mem_pow_idealOfVars_iff
∀ {σ : Type u_1} {R : Type u_2} [inst : CommSemiring R] (n : ℕ) (p : MvPolynomial σ R),
p ∈ MvPolynomial.idealOfVars σ R ^ n ↔ ∀ x ∈ p.support, n ≤ Finsupp.degree x- Defined in
- Mathlib.RingTheory.MvPolynomial.Ideal
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 91 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- CommSemiring
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Cites21
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement and proof · cited by 62,936
- Finsetstatement · cited by 13,712
- CommSemiringstatement and proof · cited by 10,911
- Finsuppstatement and proof · cited by 5,255
- Set.preimageproof · cited by 4,946
- Idealstatement and proof · cited by 4,748
- AddMonoidHomstatement · cited by 3,230
- MvPolynomialstatement and proof · cited by 2,140
- Set.Iciproof · cited by 1,070
- MvPolynomial.coeffproof · cited by 315
- MvPolynomial.supportstatement and proof · cited by 220
- AddSubmonoid.toAddSubsemigroupproof · cited by 198
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