Theorems · Definition · linear algebra

Module.Ray.map

{R : Type u_1} →
  [inst : CommSemiring R] →
    [inst_1 : PartialOrder R] →
      [inst_2 : IsStrictOrderedRing R] →
        {M : Type u_2} →
          [inst_3 : AddCommMonoid M] →
            [inst_4 : Module R M] →
              {N : Type u_3} →
                [inst_5 : AddCommMonoid N] → [inst_6 : Module R N] → (M ≃ₗ[R] N) → Module.Ray R M ≃ Module.Ray R N

An equivalence between modules implies an equivalence between rays.

Defined in

Mathlib.LinearAlgebra.Ray

Cited by

7 results in Mathlib

Foundations

Depth 30 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommSemiringPartialOrderIsStrictOrderedRingAddCommMonoidModuleAddCommMonoidModule