Theorems · Theorem · commutative algebra
Ideal.liesOver_iff
∀ {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
- 10 results in Mathlib
- Foundations
- Depth 22 from the axioms · uses propext
- Assumes
- CommSemiringSemiringAlgebra
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 and proof · cited by 170
- Ideal.LiesOver.casesOnproof · cited by 2
Cited by10
Results whose statement or proof uses this declaration.
- Ideal.IsDedekindDomain.ramificationIdx'_ne_zero_of_liesOverproof · cited by 6
- Ideal.eq_bot_of_liesOver_botproof · cited by 5
- Ideal.disjoint_primeCompl_of_liesOverproof · cited by 3
- IsLocalization.AtPrime.liesOver_map_of_liesOverproof · cited by 2
- Ideal.mem_primesOver_iff_mem_normalizedFactorsproof · cited by 2
- Ideal.liesOver_iff_dvd_mapproof · cited by 1
- Ideal.IsDedekindDomain.ramificationIdx'_le_ramificationIdx'proof · cited by 1
- Ideal.exists_relNorm_eq_pow_of_isPrimeproof · cited by 1
- Ideal.ncard_primesOver_mul_ncard_primesOverproof · cited by 0
- IsLocalization.AtPrime.mem_primesOver_of_isPrimeproof · cited by 0