Theorems · Theorem · commutative algebra
traceForm_nondegenerate
∀ (K : Type u_4) (L : Type u_5) [inst : Field K] [inst_1 : Field L] [inst_2 : Algebra K L] [FiniteDimensional K L] [Algebra.IsSeparable K L], (Algebra.traceForm K L).Nondegenerate
Let $L/K$ be a finite extension of fields. If $L/K$ is separable,
then traceForm is nondegenerate.
- Defined in
- Mathlib.RingTheory.Trace.Basic
- Cited by
- 17 results in Mathlib
- Foundations
- Depth 182 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites9
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
- FiniteDimensionalstatement and proof · cited by 1,854
- Algebra.IsSeparablestatement and proof · cited by 210
- LinearMap.BilinForm.Nondegeneratestatement · cited by 77
- Algebra.traceFormstatement and proof · cited by 33
- Module.finBasisproof · cited by 22
- det_traceForm_ne_zeroproof · cited by 1
- LinearMap.BilinForm.nondegenerate_of_det_ne_zeroproof · cited by 1
Cited by19
Results whose statement or proof uses this declaration.
- Module.Basis.traceDualproof · cited by 12
- NumberField.absNorm_differentIdealproof · cited by 4
- Algebra.discr_not_zero_of_basisproof · cited by 3
- IsIntegralClosure.isNoetherianproof · cited by 3
- Module.Basis.traceDual_eq_iffproof · cited by 2
- IsIntegralClosure.range_le_span_dualBasisstatement and proof · cited by 2
- Module.Basis.traceDual_injectiveproof · cited by 1
- Module.Basis.traceDual_repr_applyproof · cited by 1
- Module.Basis.trace_traceDual_mulproof · cited by 1
- Submodule.traceDual_span_of_basisproof · cited by 1
- traceForm_dualSubmodule_adjoinproof · cited by 1
- traceForm_nondegenerate_tfaeproof · cited by 1