Theorems · Theorem · commutative algebra
trace_eq_finrank_mul_minpoly_nextCoeff
∀ (K : Type u_4) {L : Type u_5} [inst : Field K] [inst_1 : Field L] [inst_2 : Algebra K L] [FiniteDimensional K L]
(x : L), (Algebra.trace K L) x = ↑(Module.finrank (↥K⟮x⟯) L) * -(minpoly K x).nextCoeff- Defined in
- Mathlib.RingTheory.Trace.Basic
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 135 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites18
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement and proof · cited by 62,936
- Setstatement · cited by 53,352
- RingHom.idstatement · cited by 18,349
- Algebrastatement and proof · cited by 11,388
- LinearMapstatement · cited by 10,215
- Fieldstatement and proof · cited by 7,404
- Algebra.algebraMapproof · cited by 4,706
- FiniteDimensionalstatement and proof · cited by 1,854
- Module.finrankstatement and proof · cited by 1,770
- IntermediateFieldstatement · cited by 988
- minpolystatement and proof · cited by 439
- IntermediateField.adjoinstatement and proof · cited by 382
Cited by1
Results whose statement or proof uses this declaration.
- Algebra.trace_eq_zero_of_not_isSeparableproof · cited by 2