Theorems · Theorem · commutative algebra
Ideal.comap_lt_comap_of_integral_mem_sdiff
∀ {R : Type u_1} [inst : CommRing R] {S : Type u_2} [inst_1 : CommRing S] {I J : Ideal S} [inst_2 : Algebra R S]
[hI : I.IsPrime],
I ≤ J → ∀ {x : S}, x ∈ ↑J \ ↑I → IsIntegral R x → Ideal.comap (algebraMap R S) I < Ideal.comap (algebraMap R S) J- Defined in
- Mathlib.RingTheory.Ideal.GoingUp
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 120 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites16
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement · cited by 53,352
- CommRingstatement and proof · cited by 17,173
- Algebrastatement and proof · cited by 11,388
- RingHomstatement · cited by 10,189
- SetLike.coestatement and proof · cited by 8,199
- Polynomialproof · cited by 5,681
- Idealstatement and proof · cited by 4,748
- Algebra.algebraMapstatement and proof · cited by 4,706
- Ideal.IsPrimestatement and proof · cited by 827
- Polynomial.Monicproof · cited by 461
- Ideal.comapstatement · cited by 443
- IsIntegralstatement and proof · cited by 427
Cited by2
Results whose statement or proof uses this declaration.
- Ideal.isMaximal_of_isIntegral_of_isMaximal_comapproof · cited by 5
- Ideal.IsIntegral.comap_lt_comapproof · cited by 3