Theorems · Theorem · commutative algebra
Algebra.norm_zero
∀ {R : Type u_1} {S : Type u_2} [inst : CommRing R] [inst_1 : Ring S] [inst_2 : Algebra R S] [Nontrivial S]
[Module.Free R S] [Module.Finite R S], (Algebra.norm R) 0 = 0- Defined in
- Mathlib.RingTheory.Norm.Basic
- Cited by
- 5 results in Mathlib
- Foundations
- Depth 131 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites19
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
- RingHom.idproof · cited by 18,349
- CommRingstatement and proof · cited by 17,173
- Algebrastatement and proof · cited by 11,388
- LinearMapproof · cited by 10,215
- Ringstatement and proof · cited by 7,463
- MonoidHomstatement · cited by 3,629
- Nontrivialstatement and proof · cited by 2,416
- map_zeroproof · cited by 1,614
- Module.Finitestatement and proof · cited by 1,032
- Module.Endproof · cited by 774
- Module.Freestatement and proof · cited by 597
Cited by5
Results whose statement or proof uses this declaration.
- Algebra.norm_eq_zero_iffproof · cited by 6
- Algebra.norm_invproof · cited by 2
- Algebra.intNorm_zeroproof · cited by 2
- FiniteField.norm_surjectiveproof · cited by 0
- groupCohomology.exists_mul_galRestrict_of_norm_eq_oneproof · cited by 0