Theorems · Theorem · commutative algebra
IntermediateField.AdjoinSimple.norm_gen_eq_prod_roots
∀ {K : Type u_4} {L : Type u_5} {F : Type u_6} [inst : Field K] [inst_1 : Field L] [inst_2 : Field F]
[inst_3 : Algebra K L] [inst_4 : Algebra K F] (x : L),
(Polynomial.map (algebraMap K F) (minpoly K x)).Splits →
(algebraMap K F) ((Algebra.norm K) (IntermediateField.AdjoinSimple.gen K x)) = ((minpoly K x).aroots F).prod- Defined in
- Mathlib.RingTheory.Norm.Basic
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 142 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites31
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
- Algebrastatement and proof · cited by 11,388
- RingHomstatement · cited by 10,189
- Fieldstatement and proof · cited by 7,404
- Polynomialproof · cited by 5,681
- Algebra.algebraMapstatement and proof · cited by 4,706
- MonoidHomstatement · cited by 3,629
- IntermediateFieldstatement · cited by 988
- map_oneproof · cited by 861
- Polynomial.mapstatement and proof · cited by 806
- Multiset.prodstatement and proof · cited by 528
Cited by2
Results whose statement or proof uses this declaration.
- Algebra.isIntegral_normproof · cited by 4
- Algebra.norm_eq_prod_rootsproof · cited by 1