Theorems · Theorem · commutative algebra
charP_of_injective_ringHom
∀ {R : Type u_1} {A : Type u_2} [inst : NonAssocSemiring R] [inst_1 : NonAssocSemiring A] {f : R →+* A},
Function.Injective ⇑f → ∀ (p : ℕ) [CharP R p], CharP A pIf a ring homomorphism R →+* A is injective then A has the same characteristic as R.
- Defined in
- Mathlib.Algebra.CharP.Algebra
- Cited by
- 5 results in Mathlib
- Foundations
- Depth 22 from the axioms · uses propext, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
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
- RingHomstatement and proof · cited by 10,189
- NonAssocSemiringstatement and proof · cited by 805
- CharPstatement and proof · cited by 478
- map_natCastproof · cited by 134
- map_eq_zero_iffproof · cited by 62
- CharP.cast_eq_zero_iffproof · cited by 42
Cited by5
Results whose statement or proof uses this declaration.
- expChar_of_injective_ringHomproof · cited by 8
- RingHom.charPproof · cited by 2
- charP_of_injective_algebraMapproof · cited by 2
- RingHom.charP_iffproof · cited by 1
- charP_of_injective_algebraMap'proof · cited by 0