Theorems · Theorem · commutative algebra
Ideal.map_radical_of_surjective
∀ {R : Type u_1} {S : Type u_2} [inst : CommRing R] [inst_1 : CommRing S] {f : R →+* S},
Function.Surjective ⇑f → ∀ {I : Ideal R}, RingHom.ker f ≤ I → Ideal.map f I.radical = (Ideal.map f I).radical- Defined in
- Mathlib.RingTheory.Ideal.Maps
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 84 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites24
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement and proof · cited by 62,936
- Setproof · cited by 53,352
- CommRingstatement and proof · cited by 17,173
- RingHomstatement and proof · cited by 10,189
- Set.ofPredproof · cited by 6,101
- Set.imageproof · cited by 5,609
- Idealstatement and proof · cited by 4,748
- LE.le.transproof · cited by 3,151
- Set.extproof · cited by 2,266
- le_transproof · cited by 985
- InfSet.sInfproof · cited by 935
- Ideal.IsPrimeproof · cited by 827
Cited by1
Results whose statement or proof uses this declaration.
- Ideal.radical_eq_jacobson_iff_radical_quotient_eq_jacobson_botproof · cited by 0