Theorems · Theorem · commutative algebra

MvPolynomial.weightedHomogeneousSubmodule_eq_finsupp_supported

∀ (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.weightedHomogeneousSubmodule R w m = AddMonoidAlgebra.supported R R {d | (Finsupp.weight w) d = m}

The submodule weightedHomogeneousSubmodule R w m of homogeneous MvPolynomials of degree n is equal to the R-submodule of all p : (σ →₀ ℕ) →₀ R such that p.support ⊆ {d | weight w d = m}. While equal, the former has a convenient definitional reduction.

Defined in

Mathlib.RingTheory.MvPolynomial.WeightedHomogeneous

Cited by

5 results in Mathlib

Foundations

Depth 87 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommSemiringAddCommMonoid