Theorems · Definition · commutative algebra
Ideal.under
(A : Type u_2) → [inst : CommSemiring A] → {B : Type u_3} → [inst_1 : Semiring B] → [Algebra A B] → Ideal B → Ideal AThe ideal obtained by pulling back the ideal P from B to A.
- Defined in
- Mathlib.RingTheory.Ideal.Over
- Cited by
- 170 results in Mathlib
- Foundations
- Depth 18 from the axioms, rests on 212 definitions · uses propext
- Assumes
- CommSemiringSemiringAlgebra
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites6
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
- Algebra.algebraMapproof · cited by 4,706
- Ideal.comapproof · cited by 443
Cited by186
Results whose statement or proof uses this declaration.
- Ideal.inertiaDegproof · cited by 60
- Ideal.over_defstatement · cited by 60
- Ideal.ramificationIdxproof · cited by 59
- Ideal.LiesOver.overstatement · cited by 23
- Algebra.WeaklyQuasiFiniteAtproof · cited by 18
- Localization.AtPrime.map_eq_maximalIdealproof · cited by 17
- Ideal.under_defstatement · cited by 15
- RingOfIntegers.exponentproof · cited by 15
- IsLocalization.under_map_of_isPrime_disjointstatement · cited by 15
- AlgHom.IsArithFrobAtproof · cited by 13
- IsLocalization.map_understatement and proof · cited by 12
- Ideal.LiesOver.transproof · cited by 12