Theorems · Theorem · commutative algebra
Algebra.trace_eq_zero_of_not_isSeparable
∀ {K : Type u_4} {L : Type u_5} [inst : Field K] [inst_1 : Field L] [inst_2 : Algebra K L],
¬Algebra.IsSeparable K L → Algebra.trace K L = 0- Defined in
- Mathlib.RingTheory.Trace.Basic
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 196 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites67
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- RingHom.idstatement and proof · cited by 18,349
- Finsetproof · cited by 13,712
- Algebrastatement and proof · cited by 11,388
- LinearMapstatement and proof · cited by 10,215
- Fieldstatement and proof · cited by 7,404
- Polynomialproof · cited by 5,681
- Algebra.algebraMapproof · cited by 4,706
- MulZeroClass.mul_zeroproof · cited by 2,091
- Nat.Primeproof · cited by 2,059
- FiniteDimensionalproof · cited by 1,854
- Module.finrankproof · cited by 1,770
Cited by2
Results whose statement or proof uses this declaration.
- traceForm_nondegenerate_tfaeproof · cited by 1
- dvd_differentIdeal_of_not_isSeparableproof · cited by 1