Theorems · Theorem · commutative algebra
IsLocalization.under_le_under_iff
∀ {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 ≤ J- Defined in
- Mathlib.RingTheory.Localization.Ideal
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 30 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Algebrastatement and proof · cited by 11,388
- CommSemiringstatement and proof · cited by 10,911
- Idealstatement and proof · cited by 4,748
- Submonoidstatement and proof · cited by 3,086
- IsLocalizationstatement and proof · cited by 636
- Ideal.understatement · cited by 170
- OrderEmbedding.le_iff_leproof · cited by 32
- IsLocalization.orderEmbeddingproof · cited by 4
Cited by2
Results whose statement or proof uses this declaration.
- IsLocalization.AtPrime.radical_map_of_mem_minimalPrimesproof · cited by 1
- IsLocalization.comap_le_comap_iffproof · cited by 0