Theorems · Theorem · algebraic geometry
PrimeSpectrum.t1Space_iff_isField
∀ {R : Type u} [inst : CommSemiring R] [IsDomain R], T1Space (PrimeSpectrum R) ↔ IsField R- Cited by
- 2 results in Mathlib
- Foundations
- Depth 82 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- CommSemiringIsDomain
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites14
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
- Bot.botproof · cited by 4,720
- IsDomainstatement and proof · cited by 2,196
- PrimeSpectrumstatement and proof · cited by 625
- Semifieldproof · cited by 439
- PrimeSpectrum.asIdealproof · cited by 333
- T1Spacestatement and proof · cited by 275
- IsFieldstatement and proof · cited by 103
- T1Space.t1proof · cited by 11
- Ring.ne_bot_of_isMaximal_of_not_isFieldproof · cited by 8
- PrimeSpectrum.isClosed_singleton_iff_isMaximalproof · cited by 8
- Ideal.bot_isMaximalproof · cited by 5
Cited by2
Results whose statement or proof uses this declaration.
- AlgebraicGeometry.isField_of_isIntegral_of_subsingletonproof · cited by 1
- AlgebraicGeometry.isFinite_iff_locallyOfFiniteType_of_jacobsonSpaceproof · cited by 1