Theorems · Theorem · ring theory
Subalgebra.map_injective
∀ {R : Type u} {A : Type v} {B : Type w} [inst : CommSemiring R] [inst_1 : Semiring A] [inst_2 : Algebra R A]
[inst_3 : Semiring B] [inst_4 : Algebra R B] {f : A →ₐ[R] B},
Function.Injective ⇑f → Function.Injective (Subalgebra.map f)- Defined in
- Mathlib.Algebra.Algebra.Subalgebra.Basic
- Cited by
- 5 results in Mathlib
- Foundations
- Depth 26 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites13
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
- SetLike.coeproof · cited by 8,199
- AlgHomstatement and proof · cited by 3,236
- Set.extproof · cited by 2,266
- Subalgebrastatement and proof · cited by 1,353
- Subalgebra.mapstatement and proof · cited by 90
- Set.ext_iffproof · cited by 90
- SetLike.ext_iffproof · cited by 64
- Subalgebra.extproof · cited by 28
Cited by5
Results whose statement or proof uses this declaration.
- Polynomial.Splits.adjoin_rootSet_eq_rangeproof · cited by 3
- IntermediateField.map_injectiveproof · cited by 2
- Subalgebra.fg_of_fg_mapproof · cited by 1
- Algebra.not_isStronglyTranscendental_of_weaklyQuasiFiniteAtproof · cited by 1
- Algebra.adjoin_root_eq_top_of_isSplittingFieldproof · cited by 1