Theorems · Theorem · linear algebra
Algebra.finrank_eq_one_iff_bijective_algebraMap
∀ {F : Type u_1} {E : Type u_2} [inst : CommRing F] [StrongRankCondition F] [inst_2 : Ring E] [inst_3 : Algebra F E]
[Module.Free F E], Module.finrank F E = 1 ↔ Function.Bijective ⇑(algebraMap F E)- Cited by
- 1 results in Mathlib
- Foundations
- Depth 117 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites16
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
- Algebrastatement and proof · cited by 11,388
- RingHomstatement · cited by 10,189
- Ringstatement and proof · cited by 7,463
- Algebra.algebraMapstatement and proof · cited by 4,706
- Nontrivialproof · cited by 2,416
- Module.finrankstatement and proof · cited by 1,770
- Function.Bijectivestatement and proof · cited by 863
- Module.Freestatement and proof · cited by 597
- StrongRankConditionstatement and proof · cited by 286
- FaithfulSMul.algebraMap_injectiveproof · cited by 198
Cited by1
Results whose statement or proof uses this declaration.
- bijective_algebraMap_int_of_finite_of_unramifiedproof · cited by 0