Theorems · Theorem · commutative algebra
Ideal.IsIntegral.comap_lt_comap
∀ {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) J- Defined in
- Mathlib.RingTheory.Ideal.GoingUp
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 121 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites11
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- CommRingstatement and proof · cited by 17,173
- Algebrastatement and proof · cited by 11,388
- RingHomstatement · cited by 10,189
- Idealstatement and proof · cited by 4,748
- Algebra.algebraMapstatement and proof · cited by 4,706
- Ideal.IsPrimestatement and proof · cited by 827
- Ideal.comapstatement and proof · cited by 443
- Algebra.IsIntegralstatement and proof · cited by 224
- Algebra.IsIntegral.isIntegralproof · cited by 86
- SetLike.lt_iff_le_and_existsproof · cited by 14
- Ideal.comap_lt_comap_of_integral_mem_sdiffproof · cited by 2
Cited by3
Results whose statement or proof uses this declaration.
- Ideal.IsIntegral.mem_minimalPrimes_map_underproof · cited by 0
- Ideal.IntegralClosure.comap_lt_comapproof · cited by 0
- Ideal.IsIntegralClosure.comap_le_comapproof · cited by 0