Theorems · Theorem · ring theory

LinearMap.comp_zero

∀ {R₁ : Type u_2} {R₂ : Type u_3} {R₃ : Type u_4} {M : Type u_8} {M₂ : Type u_10} {M₃ : Type u_11} [inst : Semiring R₁]
  [inst_1 : Semiring R₂] [inst_2 : Semiring R₃] [inst_3 : AddCommMonoid M] [inst_4 : AddCommMonoid M₂]
  [inst_5 : AddCommMonoid M₃] [inst_6 : Module R₁ M] [inst_7 : Module R₂ M₂] [inst_8 : Module R₃ M₃] {σ₁₂ : R₁ →+* R₂}
  {σ₂₃ : R₂ →+* R₃} {σ₁₃ : R₁ →+* R₃} [inst_9 : RingHomCompTriple σ₁₂ σ₂₃ σ₁₃] (g : M₂ →ₛₗ[σ₂₃] M₃), g ∘ₛₗ 0 = 0

Defined in

Mathlib.Algebra.Module.LinearMap.Defs

Cited by

9 results in Mathlib

Foundations

Depth 25 from the axioms · uses propext, Quot.sound

Assumes

SemiringSemiringSemiringAddCommMonoidAddCommMonoidAddCommMonoidModuleModuleModuleRingHomCompTriple