Theorems · Theorem · linear algebra
AlgHom.bijective
∀ {K : Type u_1} {S : Type u_2} [inst : Field K] [inst_1 : Ring S] [IsSimpleRing S] [inst_3 : Algebra K S]
[FiniteDimensional K S] (f : S →ₐ[K] S), Function.Bijective ⇑f- Cited by
- 2 results in Mathlib
- Foundations
- Depth 120 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites11
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement · cited by 62,936
- Algebrastatement and proof · cited by 11,388
- Ringstatement and proof · cited by 7,463
- Fieldstatement and proof · cited by 7,404
- AlgHomstatement and proof · cited by 3,236
- FiniteDimensionalstatement and proof · cited by 1,854
- Function.Bijectivestatement · cited by 863
- AlgHom.toRingHomproof · cited by 490
- RingHom.injectiveproof · cited by 187
- IsSimpleRingstatement and proof · cited by 39
- LinearMap.injective_iff_surjectiveproof · cited by 3
Cited by2
Results whose statement or proof uses this declaration.
- Matrix.det_map'proof · cited by 0
- Matrix.trace_map'proof · cited by 0