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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.

Defined in
Mathlib.RingTheory.MvPolynomial.WeightedHomogeneous
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.

MvPolynomial.homogeneousSubmodule · cited by 23MvPolynomial.homogeneousS…MvPolynomial.weightedHomogeneousSubmodule_eq_finsupp_supported · cited by 5MvPolynomial.weightedHomo…MvPolynomial.mem_weightedHomogeneousSubmodule · cited by 4MvPolynomial.mem_weighted…MvPolynomial.DirectSum.coeLinearMap_eq_dfinsuppSum · cited by 3DirectSum.coeLinearMap_eq…MvPolynomial.isWeightedHomogeneous_zero · cited by 2MvPolynomial.isWeightedHo…MvPolynomial.weightedDecomposition · cited by 2MvPolynomial.weightedDeco…MvPolynomial.weightedGradedAlgebra · cited by 2MvPolynomial.weightedGrad…MvPolynomial.IsWeightedHomogeneous.add · cited by 2IsWeightedHomogeneous.addMvPolynomial.weightedHomogeneousComponent_mem · cited by 2MvPolynomial.weightedHomo…MvPolynomial.weightedHomogeneousComponent_of_mem · cited by 2MvPolynomial.weightedHomo…MvPolynomial.weightedHomogeneousSubmodule_mul · cited by 2MvPolynomial.weightedHomo…MvPolynomial.mem_iff_weightedHomogeneousComponent_mem · cited by 2MvPolynomial.mem_iff_weig…MvPolynomial.weightedHomogeneousComponent_mem_of_mem · cited by 1MvPolynomial.weightedHomo…MvPolynomial.IsWeightedHomogeneous.pderiv · cited by 1IsWeightedHomogeneous.pde…MvPolynomial.weightedHomogeneousSubmodule_fg · cited by 1MvPolynomial.weightedHomo…AddCommMonoid · cited by 12281AddCommMonoidCommSemiring · cited by 10911CommSemiringSubmodule · cited by 7192SubmoduleSet.ofPred · cited by 6101Set.ofPredFinsupp · cited by 5255FinsuppMvPolynomial · cited by 2140MvPolynomialMvPolynomial.coeff · cited by 315MvPolynomial.coeffMvPolynomial.IsWeightedHomogeneous · cited by 31MvPolynomial.IsWeightedHo…MvPolynomial.weightedHomogene…CITED BYCITES

Cites8

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Cited by27

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