Theorems · Theorem · commutative algebra
Ideal.isPrime_of_liesOver
∀ {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.IsPrime], p.IsPrime- Defined in
- Mathlib.RingTheory.Ideal.Over
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 31 from the axioms · uses propext, Quot.sound
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.IsPrimestatement and proof · cited by 827
- Ideal.LiesOverstatement and proof · cited by 272
- Ideal.over_defproof · cited by 60
Cited by4
Results whose statement or proof uses this declaration.
- Ideal.inertiaDeg_towerproof · cited by 7
- Ideal.ramificationIdx_towerproof · cited by 5
- Ideal.absNorm_pow_inertiaDegproof · cited by 2
- Ideal.ramificationIdx'_algebra_tower'proof · cited by 1