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Theorems · Theorem · commutative algebra

RingEquiv.isLocalRing

∀ {A : Type u_4} {B : Type u_5} [inst : CommSemiring A] [IsLocalRing A] [inst_2 : Semiring B] (e : A ≃+* B),
  IsLocalRing B
Defined in
Mathlib.RingTheory.LocalRing.RingHom.Basic
Cited by
2 results in Mathlib
Foundations
Depth 29 from the axioms · uses propext, Quot.sound
Assumes
CommSemiringIsLocalRingSemiring
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Around this declaration

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

IsRegularLocalRing.of_ringEquiv · cited by 2IsRegularLocalRing.of_rin…IsDiscreteValuationRing.RingEquivClass.isDiscreteValuationRing · cited by 0RingEquivClass.isDiscrete…Semiring · cited by 13802SemiringCommSemiring · cited by 10911CommSemiringRingEquiv · cited by 1147RingEquivRingHomClass.toRingHom · cited by 746RingHomClass.toRingHomIsLocalRing · cited by 339IsLocalRingRingEquiv.surjective · cited by 28RingEquiv.surjectiveIsLocalRing.of_surjective · cited by 1IsLocalRing.of_surjectiveRingEquiv.isLocalRingCITED 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.