Mathlib Map

Theorems · Theorem · commutative algebra

MvPolynomial.isWeightedHomogeneous_zero

∀ (R : Type u_1) {M : Type u_2} [inst : CommSemiring R] {σ : Type u_3} [inst_1 : AddCommMonoid M] (w : σ → M) (m : M),
  MvPolynomial.IsWeightedHomogeneous w 0 m

0 is weighted homogeneous of any degree.

Defined in
Mathlib.RingTheory.MvPolynomial.WeightedHomogeneous
Cited by
2 results in Mathlib
Foundations
Depth 85 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
CommSemiringAddCommMonoid
Mathlib docsSourceLoogleLeanSearch

Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

MvPolynomial.IsWeightedHomogeneous.induction_on · cited by 1IsWeightedHomogeneous.ind…MvPolynomial.IsWeightedHomogeneous.pderiv · cited by 1IsWeightedHomogeneous.pde…AddCommMonoid · cited by 12281AddCommMonoidCommSemiring · cited by 10911CommSemiringFinsupp · cited by 5255FinsuppMvPolynomial · cited by 2140MvPolynomialSubmodule.zero_mem · cited by 58Submodule.zero_memMvPolynomial.IsWeightedHomogeneous · cited by 31MvPolynomial.IsWeightedHo…MvPolynomial.weightedHomogeneousSubmodule · cited by 23MvPolynomial.weightedHomo…MvPolynomial.isWeightedHomoge…CITED BYCITES

Cites7

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Cited by2

Results whose statement or proof uses this declaration.