Theorems · Theorem · commutative algebra
Ideal.IsIntegralClosure.comap_le_comap
Deprecated since 2026-05-08Use Ideal.IsIntegral.comap_lt_comap instead.
∀ {R : Type u_1} [inst : CommRing R] {A : Type u_3} [inst_1 : CommRing A] [inst_2 : Algebra R A]
[Algebra.IsIntegral R A] {I J : Ideal A} [I.IsPrime],
I < J → Ideal.comap (algebraMap R A) I < Ideal.comap (algebraMap R A) JAlias of Ideal.IsIntegral.comap_lt_comap.
- Defined in
- Mathlib.RingTheory.Ideal.GoingUp
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 122 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.
- CommRingstatement · cited by 17,173
- Algebrastatement · cited by 11,388
- RingHomstatement · cited by 10,189
- Idealstatement · cited by 4,748
- Algebra.algebraMapstatement · cited by 4,706
- Ideal.IsPrimestatement · cited by 827
- Ideal.comapstatement · cited by 443
- Algebra.IsIntegralstatement · cited by 224
- Ideal.IsIntegral.comap_lt_comapproof · cited by 3
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