Theorems · Theorem · commutative algebra
MaximalSpectrum.mk.inj
∀ {R : Type u_1} {inst : CommSemiring R} {asIdeal : Ideal R} {isMaximal : asIdeal.IsMaximal} {asIdeal_1 : Ideal R}
{isMaximal_1 : asIdeal_1.IsMaximal},
{ asIdeal := asIdeal, isMaximal := isMaximal } = { asIdeal := asIdeal_1, isMaximal := isMaximal_1 } →
asIdeal = asIdeal_1- Defined in
- Mathlib.RingTheory.Spectrum.Maximal.Defs
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 22 from the axioms · uses no axioms
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites5
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- CommSemiringstatement and proof · cited by 10,911
- Idealstatement and proof · cited by 4,748
- Ideal.IsMaximalstatement and proof · cited by 452
- MaximalSpectrumstatement · cited by 73
- MaximalSpectrum.mk.noConfusionproof · cited by 1
Cited by2
Results whose statement or proof uses this declaration.
- IsLocalRing.of_singleton_maximalSpectrumproof · cited by 2
- MaximalSpectrum.mk.injEqproof · cited by 1