Theorems · Theorem · ring theory

LinearMap.map_eq_zero_iff

∀ {R : Type u_1} {S : Type u_5} {M : Type u_8} {M₃ : Type u_11} [inst : Semiring R] [inst_1 : Semiring S]
  [inst_2 : AddCommMonoid M] [inst_3 : AddCommMonoid M₃] [inst_4 : Module R M] [inst_5 : Module S M₃] {σ : R →+* S}
  (f : M →ₛₗ[σ] M₃), Function.Injective ⇑f → ∀ {x : M}, f x = 0 ↔ x = 0

Defined in

Mathlib.Algebra.Module.LinearMap.Defs

Cited by

10 results in Mathlib

Foundations

Depth 22 from the axioms · uses propext

Assumes

SemiringSemiringAddCommMonoidAddCommMonoidModuleModule