Theorems · Theorem · commutative algebra
MvPolynomial.homogeneousComponent_mem_of_mem
∀ {σ : Type u_1} {R : Type u_3} [inst : CommSemiring R] {I : Ideal (MvPolynomial σ R)},
Ideal.IsHomogeneous (MvPolynomial.homogeneousSubmodule σ R) I →
∀ {p : MvPolynomial σ R}, p ∈ I → ∀ (n : ℕ), (MvPolynomial.homogeneousComponent n) p ∈ I- Cited by
- 0 results in Mathlib
- Foundations
- Depth 97 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- CommSemiring
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Cites13
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement · cited by 62,936
- RingHom.idstatement · cited by 18,349
- CommSemiringstatement and proof · cited by 10,911
- LinearMapstatement · cited by 10,215
- Submodulestatement · cited by 7,192
- Finsuppstatement · cited by 5,255
- Idealstatement and proof · cited by 4,748
- MvPolynomialstatement and proof · cited by 2,140
- Ideal.IsHomogeneousstatement and proof · cited by 30
- MvPolynomial.homogeneousSubmodulestatement and proof · cited by 23
- MvPolynomial.homogeneousComponentstatement · cited by 17
- MvPolynomial.gradedAlgebrastatement · cited by 2
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