Mathlib Map

Theorems · Theorem · commutative algebra

map_nonunit

∀ {R : Type u_1} {S : Type u_2} [inst : CommSemiring R] [inst_1 : IsLocalRing R] [inst_2 : CommSemiring S]
  [inst_3 : IsLocalRing S] (f : R →+* S) [IsLocalHom f],
  ∀ a ∈ IsLocalRing.maximalIdeal R, f a ∈ IsLocalRing.maximalIdeal S

The image of the maximal ideal of the source is contained within the maximal ideal of the target.

Defined in
Mathlib.RingTheory.LocalRing.RingHom.Basic
Cited by
1 results in Mathlib
Foundations
Depth 27 from the axioms · uses propext
Assumes
CommSemiringIsLocalRingCommSemiringIsLocalRingIsLocalHom
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Around this declaration

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

IsLocalRing.local_hom_TFAE · cited by 10IsLocalRing.local_hom_TFAEDFunLike.coe · cited by 62936DFunLike.coeCommSemiring · cited by 10911CommSemiringRingHom · cited by 10189RingHomIdeal · cited by 4748IdealIsUnit · cited by 1602IsUnitIsLocalRing · cited by 339IsLocalRingIsLocalRing.maximalIdeal · cited by 297IsLocalRing.maximalIdealIsLocalHom · cited by 100IsLocalHomisUnit_of_map_unit · cited by 4isUnit_of_map_unitmap_nonunitCITED BYCITES

Cites9

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Cited by1

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