Theorems · Definition · commutative algebra
LinearEquiv.smulOfUnit
{R : Type u_1} →
{M : Type u_5} → [inst : CommSemiring R] → [inst_1 : AddCommMonoid M] → [inst_2 : Module R M] → Rˣ → M ≃ₗ[R] MMultiplying by a unit a of the ring R is a linear equivalence.
- Defined in
- Mathlib.Algebra.Module.Equiv.Basic
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 26 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Modulestatement and proof · cited by 20,661
- RingHom.idstatement · cited by 18,349
- AddCommMonoidstatement and proof · cited by 12,281
- CommSemiringstatement and proof · cited by 10,911
- LinearEquivstatement · cited by 3,317
- Unitsstatement and proof · cited by 2,804
- DistribMulAction.toLinearEquivproof · cited by 8
Cited by1
Results whose statement or proof uses this declaration.
- LinearEquiv.smulOfNeZeroproof · cited by 3