Theorems · Theorem · commutative algebra
Algebra.norm_eq_zero_iff_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} [Finite ι]
[IsDomain R] [IsDomain S] (b : Module.Basis ι R S) {x : S}, (Algebra.norm R) x = 0 ↔ x = 0- Defined in
- Mathlib.RingTheory.Norm.Basic
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 133 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites14
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement · cited by 62,936
- CommRingstatement and proof · cited by 17,173
- Algebrastatement and proof · cited by 11,388
- Ringstatement and proof · cited by 7,463
- MonoidHomstatement · cited by 3,629
- Finitestatement and proof · cited by 3,029
- IsDomainstatement and proof · cited by 2,196
- Module.Basisstatement and proof · cited by 1,477
- Module.Finiteproof · cited by 1,032
- Module.Freeproof · cited by 597
- Algebra.normstatement · cited by 155
- Module.Finite.of_basisproof · cited by 22
Cited by2
Results whose statement or proof uses this declaration.
- Algebra.norm_ne_zero_iff_of_basisproof · cited by 1
- FractionalIdeal.abs_det_basis_changeproof · cited by 1