Theorems · Theorem · commutative algebra

LinearMap.range_eq_top

∀ {R : Type u_1} {R₂ : Type u_2} {M : Type u_5} {M₂ : Type u_6} [inst : Semiring R] [inst_1 : Semiring R₂]
  [inst_2 : AddCommMonoid M] [inst_3 : AddCommMonoid M₂] [inst_4 : Module R M] [inst_5 : Module R₂ M₂] {τ₁₂ : R →+* R₂}
  [inst_6 : RingHomSurjective τ₁₂] {f : M →ₛₗ[τ₁₂] M₂}, f.range = ⊤ ↔ Function.Surjective ⇑f

Defined in

Mathlib.Algebra.Module.Submodule.Range

Cited by

107 results in Mathlib

Foundations

Depth 27 from the axioms, rests on 348 definitions · uses propext, Classical.choice, Quot.sound

Assumes

SemiringSemiringAddCommMonoidAddCommMonoidModuleModuleRingHomSurjective