Theorems · Theorem · linear algebra
Module.Free.bijective_algebraMap_of_finrank_eq_one
∀ {R : Type u_1} {S : Type u_2} [inst : CommRing R] [inst_1 : Ring S] [inst_2 : Algebra R S] [Nontrivial R]
[Module.Free R S], Module.finrank R S = 1 → Function.Bijective ⇑(algebraMap R S)If S is an R-algebra that is free of rank 1 over R, the map R →+* S` is an
isomorphism.
- Defined in
- Mathlib.LinearAlgebra.Trace
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 121 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites73
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
- RingHomstatement · cited by 10,189
- Ringstatement and proof · cited by 7,463
- Algebra.algebraMapstatement and proof · cited by 4,706
- LinearEquivproof · cited by 3,317
- AlgHomproof · cited by 3,236
- one_mulproof · cited by 2,841
- Nat.cast_oneproof · cited by 2,501
Cited by1
Results whose statement or proof uses this declaration.
- Module.algebraMap_surjective_of_rankAtStalk_le_oneproof · cited by 1