Theorems · Theorem · ring theory
StarSubalgebra.map_injective
∀ {R : Type u_2} {A : Type u_3} {B : Type u_4} [inst : CommSemiring R] [inst_1 : StarRing R] [inst_2 : Semiring A]
[inst_3 : StarRing A] [inst_4 : Algebra R A] [inst_5 : StarModule R A] [inst_6 : Semiring B] [inst_7 : StarRing B]
[inst_8 : Algebra R B] [inst_9 : StarModule R B] {f : A →⋆ₐ[R] B},
Function.Injective ⇑f → Function.Injective (StarSubalgebra.map f)- Defined in
- Mathlib.Algebra.Star.Subalgebra
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 28 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
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Cites15
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
- Set.extproof · cited by 2,266
- StarRingstatement and proof · cited by 1,686
- StarModulestatement and proof · cited by 570
- StarAlgHomstatement and proof · cited by 215
- StarSubalgebrastatement and proof · cited by 194
- Set.ext_iffproof · cited by 90
- SetLike.ext_iffproof · cited by 64
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