Theorems · Theorem · ring theory
QuadraticAlgebra.algebraMap_norm_eq_mul_star
∀ {R : Type u_2} {a b : R} [inst : CommRing R] (z : QuadraticAlgebra R a b),
(algebraMap R (QuadraticAlgebra R a b)) (QuadraticAlgebra.norm z) = z * star z- Defined in
- Mathlib.Algebra.QuadraticAlgebra.Basic
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 41 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- CommRing
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
- CommRingstatement and proof · cited by 17,173
- RingHomstatement · cited by 10,189
- Algebra.algebraMapstatement and proof · cited by 4,706
- MonoidHomstatement · cited by 3,629
- add_zeroproof · cited by 2,707
- mul_commproof · cited by 2,262
- MulZeroClass.mul_zeroproof · cited by 2,091
- Nat.cast_zeroproof · cited by 1,870
- map_mulproof · cited by 1,137
- Star.starstatement · cited by 1,082
- sub_selfproof · cited by 996
Cited by4
Results whose statement or proof uses this declaration.
- QuadraticAlgebra.norm_eq_one_iff_mem_unitaryproof · cited by 3
- QuadraticAlgebra.sq_sub_trace_smul_add_norm_eq_zeroproof · cited by 1
- QuadraticAlgebra.norm_mem_nonZeroDivisors_iffproof · cited by 0
- QuadraticAlgebra.isUnit_iff_norm_isUnitproof · cited by 0