Theorems · Theorem · linear algebra
Module.rank_le_one_iff_top_isPrincipal
∀ {K : Type u} {V : Type v} [inst : Ring K] [StrongRankCondition K] [inst_2 : AddCommGroup V] [inst_3 : Module K V]
[Module.Free K V], Module.rank K V ≤ 1 ↔ ⊤.IsPrincipal- Cited by
- 1 results in Mathlib
- Foundations
- Depth 119 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites15
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Modulestatement and proof · cited by 20,661
- AddCommGroupstatement and proof · cited by 12,871
- Top.topstatement and proof · cited by 9,680
- Ringstatement and proof · cited by 7,463
- Submodulestatement · cited by 7,192
- Cardinalstatement and proof · cited by 2,598
- LinearEquiv.symmproof · cited by 1,461
- Module.Freestatement and proof · cited by 597
- Module.rankstatement and proof · cited by 496
- StrongRankConditionstatement and proof · cited by 286
- Submodule.IsPrincipalstatement · cited by 129
- Module.Free.of_equivproof · cited by 23
Cited by1
Results whose statement or proof uses this declaration.
- Module.finrank_le_one_iff_top_isPrincipalproof · cited by 1