Theorems · Theorem · ring theory
Algebra.top_toSubmodule
∀ {R : Type u} {A : Type v} [inst : CommSemiring R] [inst_1 : Semiring A] [inst_2 : Algebra R A],
Subalgebra.toSubmodule ⊤ = ⊤- Cited by
- 9 results in Mathlib
- Foundations
- Depth 75 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.
- DFunLike.coestatement · cited by 62,936
- Semiringstatement and proof · cited by 13,802
- Algebrastatement and proof · cited by 11,388
- CommSemiringstatement and proof · cited by 10,911
- Top.topstatement · cited by 9,680
- Submodulestatement · cited by 7,192
- Subalgebrastatement · cited by 1,353
- OrderEmbeddingstatement · cited by 619
- Subalgebra.toSubmodulestatement · cited by 141
Cited by9
Results whose statement or proof uses this declaration.
- Algebra.toSubmodule_eq_topproof · cited by 4
- Polynomial.IsSplittingField.finiteDimensionalproof · cited by 3
- IsCyclotomicExtension.finite_of_singletonproof · cited by 2
- exists_subalgebra_of_fgproof · cited by 1
- subalgebra_top_finrank_eq_submodule_top_finrankproof · cited by 1
- subalgebra_top_rank_eq_submodule_top_rankproof · cited by 1
- Subalgebra.fg_of_submodule_fgproof · cited by 1
- Normal.exists_isSplittingFieldproof · cited by 0
- Field.span_map_pow_expChar_pow_eq_top_of_isSeparableproof · cited by 0