Theorems · Definition · commutative algebra
MvPolynomial.weightedHomogeneousSubmodule
(R : Type u_1) →
{M : Type u_2} →
[inst : CommSemiring R] → {σ : Type u_3} → [AddCommMonoid M] → (σ → M) → M → Submodule R (MvPolynomial σ R)The submodule of homogeneous MvPolynomials of degree n.
- Cited by
- 23 results in Mathlib
- Foundations
- Depth 84 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- CommSemiringAddCommMonoid
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- AddCommMonoidstatement and proof · cited by 12,281
- CommSemiringstatement and proof · cited by 10,911
- Submodulestatement · cited by 7,192
- Set.ofPredproof · cited by 6,101
- Finsuppstatement and proof · cited by 5,255
- MvPolynomialstatement and proof · cited by 2,140
- MvPolynomial.coeffproof · cited by 315
- MvPolynomial.IsWeightedHomogeneousproof · cited by 31
Cited by27
Results whose statement or proof uses this declaration.
- MvPolynomial.homogeneousSubmoduleproof · cited by 23
- MvPolynomial.weightedHomogeneousSubmodule_eq_finsupp_supportedstatement · cited by 5
- MvPolynomial.mem_weightedHomogeneousSubmodulestatement · cited by 4
- MvPolynomial.DirectSum.coeLinearMap_eq_dfinsuppSumstatement and proof · cited by 3
- MvPolynomial.isWeightedHomogeneous_zeroproof · cited by 2
- MvPolynomial.weightedDecompositionstatement and proof · cited by 2
- MvPolynomial.weightedGradedAlgebrastatement and proof · cited by 2
- MvPolynomial.IsWeightedHomogeneous.addproof · cited by 2
- MvPolynomial.weightedHomogeneousComponent_memstatement · cited by 2
- MvPolynomial.weightedHomogeneousComponent_of_memstatement and proof · cited by 2
- MvPolynomial.weightedHomogeneousSubmodule_mulstatement and proof · cited by 2
- MvPolynomial.mem_iff_weightedHomogeneousComponent_memstatement and proof · cited by 2