Theorems · Theorem · commutative algebra

Module.Basis.traceDual_injective

∀ (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],
  Function.Injective Module.Basis.traceDual

Defined in: Mathlib.RingTheory.Trace.Basic
Cited by: 1 results in Mathlib
Foundations: Depth 184 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: Field Field Algebra FiniteDimensional Algebra.IsSeparable Finite DecidableEq

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Cites10

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

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 · cited by 1,477
Algebra.IsSeparablestatement and proof · cited by 210
traceForm_nondegenerateproof · cited by 17
Module.Basis.traceDualstatement · cited by 12
Algebra.traceForm_isSymmproof · cited by 4
LinearMap.BilinForm.dualBasis_injectiveproof · cited by 1

Cited by1

Results whose statement or proof uses this declaration.

Module.Basis.traceDual_injproof · cited by 0