Theorems · Theorem · linear algebra
subalgebra_top_rank_eq_submodule_top_rank
∀ {F : Type u_2} {E : Type u_3} [inst : CommSemiring F] [inst_1 : Semiring E] [inst_2 : Algebra F E],
Module.rank F ↥⊤ = Module.rank F ↥⊤- Cited by
- 1 results in Mathlib
- Foundations
- Depth 84 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- CommSemiringSemiringAlgebra
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites9
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Semiringstatement and proof · cited by 13,802
- Algebrastatement and proof · cited by 11,388
- CommSemiringstatement and proof · cited by 10,911
- Top.topstatement and proof · cited by 9,680
- Submodulestatement and proof · cited by 7,192
- Cardinalstatement · cited by 2,598
- Subalgebrastatement · cited by 1,353
- Module.rankstatement and proof · cited by 496
- Algebra.top_toSubmoduleproof · cited by 9
Cited by1
Results whose statement or proof uses this declaration.
- Subalgebra.rank_topproof · cited by 1