Theorems · Theorem · ring theory
Ideal.isOpen_of_isMaximal
∀ {R : Type u_1} [inst : CommRing R] [inst_1 : TopologicalSpace R] [IsTopologicalRing R] [CompactSpace R] [T2Space R]
[IsNoetherianRing R] (I : Ideal R) [I.IsMaximal], IsOpen ↑I- Defined in
- Mathlib.Topology.Algebra.Ring.Compact
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 101 from the axioms · uses propext, Classical.choice, Quot.sound
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.
- TopologicalSpacestatement and proof · cited by 24,529
- CommRingstatement and proof · cited by 17,173
- SetLike.coestatement · cited by 8,199
- Idealstatement and proof · cited by 4,748
- IsOpenstatement · cited by 2,400
- T2Spacestatement and proof · cited by 1,351
- CompactSpacestatement and proof · cited by 593
- Ideal.IsMaximalstatement and proof · cited by 452
- IsTopologicalRingstatement and proof · cited by 402
- IsNoetherianRingstatement and proof · cited by 268
- Submodule.toAddSubgroupproof · cited by 106
- AddSubgroup.FiniteIndexproof · cited by 66
Cited by1
Results whose statement or proof uses this declaration.
- IsLocalRing.isOpen_maximalIdealproof · cited by 0