Theorems · Theorem · commutative algebra
IsLocalization.comap_le_comap_iff
Deprecated since 2026-04-09Use IsLocalization.under_le_under_iff instead.
∀ {R : Type u_1} [inst : CommSemiring R] (M : Submonoid R) (S : Type u_2) [inst_1 : CommSemiring S]
[inst_2 : Algebra R S] [IsLocalization M S] {I J : Ideal S}, Ideal.under R I ≤ Ideal.under R J ↔ I ≤ JAlias of IsLocalization.under_le_under_iff.
- Defined in
- Mathlib.RingTheory.Localization.Ideal
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 31 from the axioms · uses propext, Classical.choice, Quot.sound
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Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Algebrastatement · cited by 11,388
- CommSemiringstatement · cited by 10,911
- Idealstatement · cited by 4,748
- Submonoidstatement · cited by 3,086
- IsLocalizationstatement · cited by 636
- Ideal.understatement · cited by 170
- IsLocalization.under_le_under_iffproof · cited by 2
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