Theorems · Theorem · commutative algebra
Algebra.norm_algebraMap_of_basis
∀ {R : Type u_1} {S : Type u_2} [inst : CommRing R] [inst_1 : Ring S] [inst_2 : Algebra R S] {ι : Type w}
[inst_3 : Fintype ι] (b : Module.Basis ι R S) (x : R), (Algebra.norm R) ((algebraMap R S) x) = x ^ Fintype.card ιIf x is in the base ring K, then the norm is x ^ [L : K].
- Defined in
- Mathlib.RingTheory.Norm.Defs
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 130 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites25
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
- CommRingstatement and proof · cited by 17,173
- Algebrastatement and proof · cited by 11,388
- RingHomstatement · cited by 10,189
- Fintypestatement and proof · cited by 7,736
- Ringstatement and proof · cited by 7,463
- Algebra.algebraMapstatement and proof · cited by 4,706
- MonoidHomstatement · cited by 3,629
- Module.Basisstatement and proof · cited by 1,477
- Fintype.cardstatement and proof · cited by 1,386
- Module.Endproof · cited by 774
- Matrix.detproof · cited by 665
Cited by3
Results whose statement or proof uses this declaration.
- Algebra.isIntegral_normproof · cited by 4
- Algebra.norm_eq_norm_adjoinproof · cited by 3
- ClassGroup.exists_mem_finsetApproxproof · cited by 1