Theorems · Theorem · ring theory
Subalgebra.toSubmodule_injective
∀ {R : Type u} {A : Type v} [inst : CommSemiring R] [inst_1 : Semiring A] [inst_2 : Algebra R A],
Function.Injective ⇑Subalgebra.toSubmodule- Defined in
- Mathlib.Algebra.Algebra.Subalgebra.Basic
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 30 from the axioms · uses propext, Quot.sound
- Assumes
- CommSemiringSemiringAlgebra
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites10
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement and proof · 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
- Submodulestatement · cited by 7,192
- Subalgebrastatement and proof · cited by 1,353
- OrderEmbeddingstatement · cited by 619
- Subalgebra.toSubmodulestatement and proof · cited by 141
- SetLike.extproof · cited by 92
- SetLike.ext_iffproof · cited by 64
Cited by3
Results whose statement or proof uses this declaration.
- Subalgebra.eq_of_le_of_finrank_leproof · cited by 2
- Algebra.map_botproof · cited by 1
- Field.Emb.Cardinal.adjoin_basis_eq_topproof · cited by 0