Theorems · Theorem · commutative algebra

PolynomialModule.hom_ext

∀ {R : Type u_2} {M : Type u_3} [inst : CommRing R] [inst_1 : AddCommGroup M] [inst_2 : Module R M] {M' : Type u_7}
  [inst_3 : AddCommGroup M'] [inst_4 : Module R M'] {f g : PolynomialModule R M →ₗ[R] M'},
  (∀ (a : ℕ), f ∘ₗ PolynomialModule.lsingle R a = g ∘ₗ PolynomialModule.lsingle R a) → f = g

Two R-linear maps from PolynomialModule R M which are equal after pre-composition with every lsingle R a are equal.

Defined in

Mathlib.Algebra.Polynomial.Module.Basic

Cited by

1 results in Mathlib

Foundations

Depth 82 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommRingAddCommGroupModuleAddCommGroupModule