Theorems · Theorem · ring theory

Module.Finite.of_isComplemented_domain

∀ {R : Type u_2} [inst : Ring R] {M : Type u_4} [inst_1 : AddCommGroup M] [inst_2 : Module R M] {m : Submodule R M}
  (R₀ : Type u_6) (P : Type u_7) [inst_3 : Semiring R₀] [inst_4 : AddCommMonoid P] [inst_5 : Module R P]
  [inst_6 : Module R₀ P] [inst_7 : SMulCommClass R R₀ P] [Module.Finite R₀ (M →ₗ[R] P)],
  IsComplemented m → Module.Finite R₀ (↥m →ₗ[R] P)

Defined in

Mathlib.RingTheory.SimpleModule.Basic

Cited by

0 results in Mathlib

Foundations

Depth 81 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

RingAddCommGroupModuleSemiringAddCommMonoidModuleModuleSMulCommClassModule.Finite