Theorems · Theorem · commutative algebra
Ideal.comap_surjective_of_faithfullyFlat
∀ {A : Type u_1} {B : Type u_2} [inst : CommRing A] [inst_1 : CommRing B] [inst_2 : Algebra A B]
[Module.FaithfullyFlat A B], Function.Surjective (Ideal.comap (algebraMap A B))If B is a faithfully-flat A-algebra, every ideal in A is the preimage of some ideal
in B.
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- Foundations
- Depth 111 from the axioms · uses propext, Classical.choice, Quot.sound
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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
- RingHomstatement · cited by 10,189
- Idealstatement and proof · cited by 4,748
- Algebra.algebraMapstatement and proof · cited by 4,706
- Ideal.mapproof · cited by 692
- Ideal.comapstatement · cited by 443
- Module.FaithfullyFlatstatement and proof · cited by 72
- Ideal.comap_map_eq_self_of_faithfullyFlatproof · cited by 4
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