Theorems · Theorem · commutative algebra
Ideal.IsMaximal.of_liesOver_isMaximal
∀ {A : Type u_1} [inst : CommRing A] {B : Type u_2} [inst_1 : CommRing B] [inst_2 : Algebra A B]
[Algebra.IsIntegral A B] (P : Ideal B) (p : Ideal A) [P.LiesOver p] [hpm : p.IsMaximal] [P.IsPrime], P.IsMaximal- Defined in
- Mathlib.RingTheory.Ideal.GoingUp
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 122 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites9
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
- Idealstatement and proof · cited by 4,748
- Ideal.IsPrimestatement and proof · cited by 827
- Ideal.IsMaximalstatement and proof · cited by 452
- Ideal.LiesOverstatement and proof · cited by 272
- Algebra.IsIntegralstatement and proof · cited by 224
- Ideal.over_defproof · cited by 60
- Ideal.isMaximal_of_isIntegral_of_isMaximal_comapproof · cited by 5
Cited by4
Results whose statement or proof uses this declaration.
- IsCyclotomicExtension.Rat.inertiaDeg_span_zeta_sub_oneproof · cited by 4
- Ideal.absNorm_pow_inertiaDegproof · cited by 2
- IsCyclotomicExtension.Rat.inertiaDeg_eq_of_not_dvdproof · cited by 1
- Ideal.relNorm_eq_pow_of_isPrime_isGaloisproof · cited by 1