Theorems · Theorem · ring theory
IsLocalRing.isOpen_maximalIdeal_pow
∀ (R : Type u_1) [inst : CommRing R] [inst_1 : TopologicalSpace R] [IsTopologicalRing R] [CompactSpace R] [T2Space R] [inst_5 : IsLocalRing R] [IsNoetherianRing R] (n : ℕ), IsOpen ↑(IsLocalRing.maximalIdeal R ^ n)
- Defined in
- Mathlib.Topology.Algebra.Ring.Compact
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 103 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites12
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 · cited by 4,748
- IsOpenstatement · cited by 2,400
- T2Spacestatement and proof · cited by 1,351
- CompactSpacestatement and proof · cited by 593
- IsTopologicalRingstatement and proof · cited by 402
- IsLocalRingstatement and proof · cited by 339
- IsLocalRing.maximalIdealstatement and proof · cited by 297
- IsNoetherianRingstatement and proof · cited by 268
- Ideal.isOpen_pow_of_isMaximalproof · cited by 1
Cited by1
Results whose statement or proof uses this declaration.
- IsLocalRing.isOpen_iff_finite_quotientproof · cited by 0