Theorems · Theorem · commutative algebra

Algebra.trace_algebraMap_of_basis

∀ {R : Type u_1} {S : Type u_2} [inst : CommRing R] [inst_1 : CommRing S] [inst_2 : Algebra R S] {ι : Type w}
  [inst_3 : Fintype ι] (b : Module.Basis ι R S) (x : R), (Algebra.trace R S) ((algebraMap R S) x) = Fintype.card ι • x

If x is in the base field K, then the trace is [L : K] * x.

Defined in

Mathlib.RingTheory.Trace.Defs

Cited by

2 results in Mathlib

Foundations

Depth 94 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommRingCommRingAlgebraFintype