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Theorems · Definition · commutative algebra

MvPolynomial.weightedDecomposition

(R : Type u_1) →
  {M : Type u_2} →
    [inst : CommSemiring R] →
      {σ : Type u_3} →
        (w : σ → M) →
          [inst_1 : AddCommMonoid M] →
            [inst_2 : DecidableEq M] → DirectSum.Decomposition (MvPolynomial.weightedHomogeneousSubmodule R w)

Given a weight w, the decomposition of MvPolynomial σ R into weighted homogeneous submodules

Defined in
Mathlib.RingTheory.MvPolynomial.WeightedHomogeneous
Cited by
2 results in Mathlib
Foundations
Depth 92 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
CommSemiringAddCommMonoidDecidableEq
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Around this declaration

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

MvPolynomial.weightedGradedAlgebra · cited by 2MvPolynomial.weightedGrad…MvPolynomial.weightedDecomposition.decompose'_apply · cited by 1weightedDecomposition.dec…MvPolynomial.weightedDecomposition.decompose'_eq · cited by 0weightedDecomposition.dec…AddCommMonoid · cited by 12281AddCommMonoidCommSemiring · cited by 10911CommSemiringSubmodule · cited by 7192SubmoduleFinsupp · cited by 5255FinsuppMvPolynomial · cited by 2140MvPolynomialDirectSum · cited by 446DirectSumDirectSum.Decomposition · cited by 57DirectSum.DecompositionMvPolynomial.weightedHomogeneousSubmodule · cited by 23MvPolynomial.weightedHomo…MvPolynomial.decompose' · cited by 1MvPolynomial.decompose'MvPolynomial.weightedDecompos…CITED BYCITES

Cites9

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Cited by3

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