Theorems · Theorem · commutative algebra
LinearMap.det_restrictScalars
∀ {R : Type u_1} {S : Type u_2} {A : Type u_3} [inst : CommRing R] [inst_1 : CommRing S] [inst_2 : Algebra R S]
[Module.Free R S] [inst_4 : AddCommGroup A] [inst_5 : Module R A] [inst_6 : Module S A] [inst_7 : IsScalarTower R S A]
[Module.Free S A] {f : A →ₗ[S] A}, LinearMap.det (↑R f) = (Algebra.norm R) (LinearMap.det f)- Defined in
- Mathlib.RingTheory.Norm.Transitivity
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 131 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites41
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement and proof · cited by 62,936
- Modulestatement and proof · cited by 20,661
- RingHom.idstatement and proof · cited by 18,349
- CommRingstatement and proof · cited by 17,173
- AddCommGroupstatement and proof · cited by 12,871
- Algebrastatement and proof · cited by 11,388
- LinearMapstatement and proof · cited by 10,215
- Fintypeproof · cited by 7,736
- Matrixproof · cited by 4,303
- IsScalarTowerstatement and proof · cited by 3,896
- MonoidHomstatement · cited by 3,629
- Nontrivialproof · cited by 2,416
Cited by2
Results whose statement or proof uses this declaration.
- Algebra.norm_normproof · cited by 5
- UpperHalfPlane.det_smulFDerivproof · cited by 0