Theorems · Theorem · linear algebra
Module.rank_eq_one_iff_finrank_eq_one
∀ {R : Type u} {M : Type v} [inst : Semiring R] [inst_1 : AddCommMonoid M] [inst_2 : Module R M],
Module.rank R M = 1 ↔ Module.finrank R M = 1- Defined in
- Mathlib.LinearAlgebra.Dimension.Finrank
- Cited by
- 8 results in Mathlib
- Foundations
- Depth 92 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- SemiringAddCommMonoidModule
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
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
- Semiringstatement and proof · cited by 13,802
- AddCommMonoidstatement and proof · cited by 12,281
- Cardinalstatement · cited by 2,598
- Module.finrankstatement · cited by 1,770
- Module.rankstatement · cited by 496
- Cardinal.toNat_eq_oneproof · cited by 4
Cited by8
Results whose statement or proof uses this declaration.
- LinearEquiv.mem_dilatransvections_iff_rankproof · cited by 2
- IntermediateField.finrank_topproof · cited by 2
- CuspForm.exists_smul_discriminant_of_weight_eq_twelveproof · cited by 1
- MvPolynomial.finrank_eq_oneproof · cited by 0
- Module.Invertible.rank_eq_oneproof · cited by 0
- Module.rank_of_bijective_algebraMapproof · cited by 0
- Module.rank_of_bijective_toSpanSingletonproof · cited by 0
- InnerProductSpace.rank_rankOneproof · cited by 0