Theorems · Theorem · linear algebra
CommSemiring.finrank_self
∀ (R : Type u_1) [inst : CommSemiring R], Module.finrank R R = 1
- Defined in
- Mathlib.LinearAlgebra.Dimension.Finrank
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 93 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- CommSemiring
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites4
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- CommSemiringstatement and proof · cited by 10,911
- Module.finrankstatement · cited by 1,770
- Module.finrank_eq_of_rank_eqproof · cited by 13
- CommSemiring.rank_selfproof · cited by 2
Cited by3
Results whose statement or proof uses this declaration.
- Module.Invertible.finrank_eq_oneproof · cited by 2
- AlgebraicGeometry.Scheme.Hom.residueDegree_idproof · cited by 1
- Representation.IsIrreducible.finrank_intertwiningMap_selfproof · cited by 1