Theorems · Theorem · commutative algebra

Algebra.trace_eq_matrix_trace

∀ {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] [inst_4 : DecidableEq ι] (b : Module.Basis ι R S) (s : S),
  (Algebra.trace R S) s = ((Algebra.leftMulMatrix b) s).trace

Defined in

Mathlib.RingTheory.Trace.Defs

Cited by

9 results in Mathlib

Foundations

Depth 95 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommRingCommRingAlgebraFintypeDecidableEq