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Theorems · Theorem · commutative algebra

RingHom.charP

∀ {R : Type u_1} {A : Type u_2} [inst : NonAssocSemiring R] [inst_1 : NonAssocSemiring A] (f : R →+* A),
  Function.Injective ⇑f → ∀ (p : ℕ) [CharP A p], CharP R p

If R →+* A is injective, and A is of characteristic p, then R is also of characteristic p. Similar to RingHom.charZero.

Defined in
Mathlib.Algebra.CharP.Algebra
Cited by
2 results in Mathlib
Foundations
Depth 31 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
NonAssocSemiringNonAssocSemiringCharP
Mathlib docsSourceLoogleLeanSearch

Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

RingHom.expChar · cited by 1RingHom.expCharRingHom.charP_iff · cited by 1RingHom.charP_iffDFunLike.coe · cited by 62936DFunLike.coeRingHom · cited by 10189RingHomNonAssocSemiring · cited by 805NonAssocSemiringCharP · cited by 478CharPCharP.exists · cited by 16CharP.existsCharP.eq · cited by 9CharP.eqcharP_of_injective_ringHom · cited by 5charP_of_injective_ringHomRingHom.charPCITED BYCITES

Cites7

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Cited by2

Results whose statement or proof uses this declaration.