Theorems · Theorem · commutative algebra

MvPolynomial.weightedHomogeneousSubmodule_fg

∀ (R : Type u_1) [inst : CommSemiring R] {σ : Type u_3} [Finite σ] (w : σ → ℕ),
  (∀ (x : σ), w x ≠ 0) → ∀ (n : ℕ), (MvPolynomial.weightedHomogeneousSubmodule R w n).FG

Defined in: Mathlib.RingTheory.MvPolynomial.WeightedHomogeneous
Cited by: 1 results in Mathlib
Foundations: Depth 88 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: CommSemiring Finite

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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
CommSemiringstatement and proof · cited by 10,911
Submoduleproof · cited by 7,192
Set.Elemproof · cited by 7,166
Set.ofPredproof · cited by 6,101
Finsuppstatement and proof · cited by 5,255
Finitestatement and proof · cited by 3,029
MvPolynomialstatement and proof · cited by 2,140
Submodule.FGstatement and proof · cited by 230
Finsupp.weightproof · cited by 90
Set.Finite.to_subtypeproof · cited by 44
MvPolynomial.weightedHomogeneousSubmodulestatement · cited by 23

Cited by1

Results whose statement or proof uses this declaration.

MvPolynomial.homogeneousSubmodule_fgproof · cited by 0