Theorems · Theorem · commutative algebra
Ideal.over_def
∀ {A : Type u_2} [inst : CommSemiring A] {B : Type u_3} [inst_1 : Semiring B] [inst_2 : Algebra A B] (P : Ideal B)
(p : Ideal A) [P.LiesOver p], p = Ideal.under A P- Defined in
- Mathlib.RingTheory.Ideal.Over
- Cited by
- 60 results in Mathlib
- Foundations
- Depth 20 from the axioms · uses propext
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Semiringstatement and proof · cited by 13,802
- Algebrastatement and proof · cited by 11,388
- CommSemiringstatement and proof · cited by 10,911
- Idealstatement and proof · cited by 4,748
- Ideal.LiesOverstatement and proof · cited by 272
- Ideal.understatement · cited by 170
- Ideal.LiesOver.overproof · cited by 23
Cited by61
Results whose statement or proof uses this declaration.
- Ideal.LiesOver.transproof · cited by 12
- Ideal.inertiaDeg'_algebraMapproof · cited by 11
- Ideal.ramificationIdx_eqproof · cited by 6
- Ideal.inertiaDeg_eqproof · cited by 6
- Ideal.exists_smul_eq_of_isGaloisGroupproof · cited by 6
- Ideal.fiberIsoOfBijectiveResidueFieldstatement · cited by 5
- Ideal.isPrime_of_liesOverproof · cited by 4
- Ideal.IsMaximal.of_liesOver_isMaximalproof · cited by 4
- Ideal.ne_bot_of_liesOver_of_ne_botproof · cited by 4
- Ideal.ramificationIdx'_eq_ramificationIdx'proof · cited by 3
- Ideal.comap_fiberIsoOfBijectiveResidueField_symmstatement and proof · cited by 2
- Ideal.eq_top_iff_of_liesOverproof · cited by 2