Theorems · Theorem · ring theory
Ideal.isOpen_pow_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] (n : ℕ), IsOpen ↑(I ^ n)- Defined in
- Mathlib.Topology.Algebra.Ring.Compact
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 102 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites17
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
- IsCompact.isClosedproof · cited by 77
Cited by1
Results whose statement or proof uses this declaration.
- IsLocalRing.isOpen_maximalIdeal_powproof · cited by 1