Theorems · Theorem · commutative algebra

IsBaseChange.det_endHom

∀ {R : Type u_6} [inst : CommRing R] (S : Type u_7) [inst_1 : CommRing S] [inst_2 : Algebra R S] (M : Type u_8)
  [inst_3 : AddCommGroup M] [inst_4 : Module R M] {P : Type u_9} [inst_5 : AddCommGroup P] [inst_6 : Module R P]
  [inst_7 : Module S P] [inst_8 : IsScalarTower R S P] [Module.Free R M] [Module.Finite R M] {α : M →ₗ[R] P}
  (j : IsBaseChange S α) (f : M →ₗ[R] M), LinearMap.det (j.endHom f) = (algebraMap R S) (LinearMap.det f)

Defined in

Mathlib.RingTheory.TensorProduct.IsBaseChangeHom

Cited by

1 results in Mathlib

Foundations

Depth 130 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommRingCommRingAlgebraAddCommGroupModuleAddCommGroupModuleModuleIsScalarTowerModule.FreeModule.Finite