Theorems · Theorem · commutative algebra
Ideal.minimalPrimes_comap_of_surjective
∀ {R : Type u_1} {S : Type u_2} [inst : CommRing R] [inst_1 : CommRing S] {f : R →+* S},
Function.Surjective ⇑f → ∀ {I J : Ideal S}, J ∈ I.minimalPrimes → Ideal.comap f J ∈ (Ideal.comap f I).minimalPrimes- Cited by
- 3 results in Mathlib
- Foundations
- Depth 76 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites21
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
- Setstatement · cited by 53,352
- CommRingstatement and proof · cited by 17,173
- RingHomstatement and proof · cited by 10,189
- Idealstatement and proof · cited by 4,748
- LE.le.transproof · cited by 3,151
- Ideal.IsPrimeproof · cited by 827
- Ideal.mapproof · cited by 692
- Ideal.comapstatement and proof · cited by 443
- RingHom.kerproof · cited by 363
- bot_leproof · cited by 306
- Ideal.minimalPrimesstatement and proof · cited by 74
Cited by3
Results whose statement or proof uses this declaration.
- Ideal.comap_minimalPrimes_eq_of_surjectiveproof · cited by 3
- Ideal.mem_minimalPrimes_span_of_mem_minimalPrimes_span_insertproof · cited by 1
- Ideal.minimal_primes_comap_of_surjectiveproof · cited by 0