Theorems · Definition · commutative algebra

LinearEquiv.ofSubsingleton

{R : Type u_1} →
  (M : Type u_5) →
    (M₂ : Type u_7) →
      [inst : Semiring R] →
        [inst_1 : AddCommMonoid M] →
          [inst_2 : AddCommMonoid M₂] →
            [inst_3 : Module R M] → [inst_4 : Module R M₂] → [Subsingleton M] → [Subsingleton M₂] → M ≃ₗ[R] M₂

Any two modules that are subsingletons are isomorphic.

Defined in

Mathlib.Algebra.Module.Equiv.Basic

Cited by

6 results in Mathlib

Foundations

Depth 21 from the axioms · uses propext, Quot.sound

Assumes

SemiringAddCommMonoidAddCommMonoidModuleModuleSubsingletonSubsingleton