Theorems · Theorem · linear algebra
Subalgebra.rank_bot
∀ {F : Type u_2} {E : Type u_3} [inst : CommRing F] [IsDomain F] [inst_2 : Ring E] [inst_3 : Algebra F E]
[StrongRankCondition F] [Module.IsTorsionFree F E] [Nontrivial E], Module.rank F ↥⊥ = 1- Cited by
- 1 results in Mathlib
- Foundations
- Depth 115 from the axioms · uses propext, Classical.choice, Quot.sound
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.
- CommRingstatement and proof · cited by 17,173
- Algebrastatement and proof · cited by 11,388
- Ringstatement and proof · cited by 7,463
- Submoduleproof · cited by 7,192
- Bot.botstatement and proof · cited by 4,720
- Cardinalstatement and proof · cited by 2,598
- Nontrivialstatement and proof · cited by 2,416
- IsDomainstatement and proof · cited by 2,196
- LinearEquiv.symmproof · cited by 1,461
- Subalgebrastatement · cited by 1,353
- one_ne_zeroproof · cited by 885
- Module.IsTorsionFreestatement and proof · cited by 600
Cited by1
Results whose statement or proof uses this declaration.
- Subalgebra.finrank_botproof · cited by 0