Theorems · Theorem · commutative algebra

Module.Finite.of_surjective

∀ {R : Type u_1} {M : Type u_4} [inst : Semiring R] [inst_1 : AddCommMonoid M] [inst_2 : Module R M] {S : Type u_7}
  {P : Type u_6} [inst_3 : Semiring S] [inst_4 : AddCommMonoid P] [inst_5 : Module S P] {σ : R →+* S}
  [hM : Module.Finite R M] (f : M →ₛₗ[σ] P), Function.Surjective ⇑f → Module.Finite S P

[Stacks Tag 0519](https://stacks.math.columbia.edu/tag/0519) ((3))

Defined in

Mathlib.RingTheory.Finiteness.Basic

Cited by

29 results in Mathlib

Foundations

Depth 80 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

SemiringAddCommMonoidModuleSemiringAddCommMonoidModuleModule.Finite