Theorems · Theorem · linear algebra
Subalgebra.bot_eq_top_iff_rank_eq_one
∀ {F : Type u_1} {E : Type u_2} [inst : CommRing F] [StrongRankCondition F] [inst_2 : Ring E] [inst_3 : Algebra F E]
[Nontrivial E] [Module.Free F E], ⊥ = ⊤ ↔ Module.rank F E = 1- Cited by
- 2 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.
Cites17
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
- Top.topstatement and proof · cited by 9,680
- Ringstatement and proof · cited by 7,463
- Bot.botstatement and proof · cited by 4,720
- Cardinalstatement and proof · cited by 2,598
- Nontrivialstatement and proof · cited by 2,416
- LinearEquiv.symmproof · cited by 1,461
- Subalgebrastatement · cited by 1,353
- Module.Freestatement and proof · cited by 597
- Module.rankstatement · cited by 496
- StrongRankConditionstatement and proof · cited by 286
Cited by2
Results whose statement or proof uses this declaration.
- IntermediateField.rank_topproof · cited by 4
- Subalgebra.bot_eq_top_of_rank_eq_oneproof · cited by 0