Theorems · Theorem · commutative algebra

HahnModule.coeff_smul_left

∀ {Γ : Type u_1} {Γ' : Type u_2} {R : Type u_3} {V : Type u_5} [inst : PartialOrder Γ] [inst_1 : PartialOrder Γ']
  [inst_2 : VAdd Γ Γ'] [inst_3 : IsOrderedCancelVAdd Γ Γ'] [inst_4 : AddCommMonoid V] [inst_5 : Zero R]
  [inst_6 : SMulWithZero R V] {x : HahnSeries Γ R} {y : HahnModule Γ' R V} {a : Γ'} {s : Set Γ} (hs : s.IsPWO),
  x.support ⊆ s →
    ((HahnModule.of R).symm (x • y)).coeff a =
      ∑ ij ∈ Finset.VAddAntidiagonal a ⋯, x.coeff ij.1 • ((HahnModule.of R).symm y).coeff ij.2

Defined in

Mathlib.RingTheory.HahnSeries.Multiplication

Cited by

2 results in Mathlib

Foundations

Depth 94 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

PartialOrderPartialOrderVAddIsOrderedCancelVAddAddCommMonoidZeroSMulWithZero