Theorems · Theorem · commutative algebra
Ideal.minimalPrimes_eq_comap
∀ {R : Type u_1} [inst : CommRing R] {I : Ideal R},
I.minimalPrimes = Ideal.comap (Ideal.Quotient.mk I) '' minimalPrimes (R ⧸ I)- Cited by
- 2 results in Mathlib
- Foundations
- Depth 87 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- CommRing
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites15
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement and proof · cited by 53,352
- CommRingstatement and proof · cited by 17,173
- RingHomstatement · cited by 10,189
- Set.imagestatement and proof · cited by 5,609
- Idealstatement and proof · cited by 4,748
- Bot.botproof · cited by 4,720
- HasQuotient.Quotientstatement and proof · cited by 2,301
- Ideal.Quotient.mkstatement and proof · cited by 610
- Ideal.comapstatement and proof · cited by 443
- Ideal.Quotient.mk_surjectiveproof · cited by 134
- Ideal.minimalPrimesstatement and proof · cited by 74
- Ideal.mk_kerproof · cited by 59
Cited by2
Results whose statement or proof uses this declaration.
- isDedekindDomainDvr.of_formallyUnramifiedproof · cited by 1
- Ideal.krullDimLE_zero_quotient_iff_forall_minimalPrimes_isMaximalproof · cited by 0