Theorems · Theorem · commutative algebra
IntermediateField.AdjoinSimple.trace_gen_eq_zero
∀ {K : Type u_4} {L : Type u_5} [inst : Field K] [inst_1 : Field L] [inst_2 : Algebra K L] {x : L},
¬IsIntegral K x → (Algebra.trace K ↥K⟮x⟯) (IntermediateField.AdjoinSimple.gen K x) = 0- Defined in
- Mathlib.RingTheory.Trace.Basic
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 132 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites22
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 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
- Module.Basisproof · cited by 1,477
- IntermediateFieldstatement · cited by 988
- IsIntegralstatement and proof · cited by 427
- IntermediateField.adjoinstatement and proof · cited by 382
- Set.mem_singletonproof · cited by 183
Cited by1
Results whose statement or proof uses this declaration.
- IntermediateField.AdjoinSimple.trace_gen_eq_sum_rootsproof · cited by 1