Theorems · Theorem · linear algebra
Subalgebra.finrank_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.finrank F ↥⊥ = 1- Cited by
- 0 results in Mathlib
- Foundations
- Depth 116 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites13
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
- Bot.botstatement · cited by 4,720
- Nat.cast_oneproof · cited by 2,501
- Nontrivialstatement and proof · cited by 2,416
- IsDomainstatement and proof · cited by 2,196
- Module.finrankstatement · cited by 1,770
- Subalgebrastatement · cited by 1,353
- Module.IsTorsionFreestatement and proof · cited by 600
- StrongRankConditionstatement and proof · cited by 286
- Module.finrank_eq_of_rank_eqproof · cited by 13
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