Theorems · Theorem · commutative algebra
Ideal.comap_ne_bot_of_algebraic_mem
∀ {R : Type u_1} [inst : CommRing R] {S : Type u_2} [inst_1 : CommRing S] {I : Ideal S} [inst_2 : Algebra R S]
[IsDomain S] {x : S}, x ≠ 0 → x ∈ I → IsAlgebraic R x → Ideal.comap (algebraMap R S) I ≠ ⊥- Defined in
- Mathlib.RingTheory.Ideal.GoingUp
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 119 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites13
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- CommRingstatement and proof · cited by 17,173
- Algebrastatement and proof · cited by 11,388
- RingHomstatement · cited by 10,189
- Polynomialproof · cited by 5,681
- Idealstatement and proof · cited by 4,748
- Bot.botstatement and proof · cited by 4,720
- Algebra.algebraMapstatement and proof · cited by 4,706
- IsDomainstatement and proof · cited by 2,196
- Polynomial.aevalproof · cited by 615
- Ideal.comapstatement and proof · cited by 443
- IsAlgebraicstatement and proof · cited by 163
Cited by1
Results whose statement or proof uses this declaration.
- Ideal.comap_ne_bot_of_integral_memproof · cited by 2