Theorems · Theorem · commutative algebra

Module.Basis.traceDual_inj

∀ {K : Type u_4} {L : Type u_5} [inst : Field K] [inst_1 : Field L] [inst_2 : Algebra K L] {ι : Type w}
  [inst_3 : FiniteDimensional K L] [inst_4 : Algebra.IsSeparable K L] [inst_5 : Finite ι] [inst_6 : DecidableEq ι]
  {b b' : Module.Basis ι K L}, b.traceDual = b'.traceDual ↔ b = b'

Defined in: Mathlib.RingTheory.Trace.Basic
Cited by: 0 results in Mathlib
Foundations: Depth 185 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: Field Field Algebra FiniteDimensional Algebra.IsSeparable Finite DecidableEq

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Algebrastatement and proof · cited by 11,388
Fieldstatement and proof · cited by 7,404
Finitestatement and proof · cited by 3,029
FiniteDimensionalstatement and proof · cited by 1,854
Module.Basisstatement and proof · cited by 1,477
Algebra.IsSeparablestatement and proof · cited by 210
Module.Basis.traceDualstatement · cited by 12
Module.Basis.traceDual_injectiveproof · cited by 1

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