Theorems · Theorem · functional analysis
Ideal.IsMaximal.closure_eq
∀ {R : Type u_1} [inst : NormedRing R] [HasSummableGeomSeries R] {I : Ideal R}, I.IsMaximal → I.closure = IThe Ideal.closure of a maximal ideal in a normed ring with summable
geometric series is the ideal itself.
- Defined in
- Mathlib.Analysis.Normed.Ring.Units
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 176 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites9
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Idealstatement and proof · cited by 4,748
- NormedRingstatement and proof · cited by 924
- Ideal.IsMaximalstatement and proof · cited by 452
- subset_closureproof · cited by 309
- HasSummableGeomSeriesstatement and proof · cited by 60
- Ideal.IsMaximal.ne_topproof · cited by 42
- Ideal.IsMaximal.eq_of_leproof · cited by 39
- Ideal.closurestatement · cited by 8
- Ideal.closure_ne_topproof · cited by 1
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