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Theorems · Theorem · commutative algebra

RingHom.charP_iff

∀ {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 p

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

Defined in
Mathlib.Algebra.CharP.Algebra
Cited by
1 results in Mathlib
Foundations
Depth 32 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
NonAssocSemiringNonAssocSemiring
Mathlib docsSourceLoogleLeanSearch

Around this declaration

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

CharP.charP_center_iff · cited by 0CharP.charP_center_iffDFunLike.coe · cited by 62936DFunLike.coeRingHom · cited by 10189RingHomNonAssocSemiring · cited by 805NonAssocSemiringCharP · cited by 478CharPcharP_of_injective_ringHom · cited by 5charP_of_injective_ringHomRingHom.charP · cited by 2RingHom.charPRingHom.charP_iffCITED BYCITES

Cites6

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Cited by1

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