Theorems · Theorem · commutative algebra
charP_of_injective_algebraMap
∀ {R : Type u_1} {A : Type u_2} [inst : CommSemiring R] [inst_1 : Semiring A] [inst_2 : Algebra R A],
Function.Injective ⇑(algebraMap R A) → ∀ (p : ℕ) [CharP R p], CharP A pIf the algebra map R →+* A is injective then A has the same characteristic as R.
- Defined in
- Mathlib.Algebra.CharP.Algebra
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 23 from the axioms · uses propext, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
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
- RingHomstatement · cited by 10,189
- Algebra.algebraMapstatement and proof · cited by 4,706
- CharPstatement and proof · cited by 478
- charP_of_injective_ringHomproof · cited by 5
Cited by2
Results whose statement or proof uses this declaration.
- algebraRat.charP_zeroproof · cited by 0
- IsFractionRing.charP_of_isFractionRingproof · cited by 0