Mathlib Map

Theorems · Definition · commutative algebra

Ideal.mapHom

{R : Type u} →
  {S : Type v} →
    {F : Type u_1} →
      [inst : CommSemiring R] →
        [inst_1 : CommSemiring S] → [inst_2 : FunLike F R S] → [rc : RingHomClass F R S] → F → Ideal R →+* Ideal S

The pushforward Ideal.map as a (semi)ring homomorphism.

Defined in
Mathlib.RingTheory.Ideal.Maps
Cited by
2 results in Mathlib
Foundations
Depth 77 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
CommSemiringCommSemiringFunLikeRingHomClass
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Around this declaration

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

Ideal.map_pow · cited by 17Ideal.map_powIdeal.mapHom_apply · cited by 0Ideal.mapHom_applyCommSemiring · cited by 10911CommSemiringRingHom · cited by 10189RingHomIdeal · cited by 4748IdealFunLike · cited by 2560FunLikeIdeal.map · cited by 692Ideal.mapRingHomClass · cited by 193RingHomClassIdeal.mapHomCITED BYCITES

Cites6

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.