Theorems · Theorem · commutative algebra
IsLocalRing.quotient_artinian_of_mem_minimalPrimes_of_isLocalRing
∀ {R : Type u_1} [inst : CommRing R] [IsNoetherianRing R] [inst_2 : IsLocalRing R] (I : Ideal R),
IsLocalRing.maximalIdeal R ∈ I.minimalPrimes → IsArtinianRing (R ⧸ I)- Cited by
- 1 results in Mathlib
- Foundations
- Depth 135 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites26
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
- Semiringproof · cited by 13,802
- Idealstatement and proof · cited by 4,748
- Algebra.algebraMapproof · cited by 4,706
- LE.le.transproof · cited by 3,151
- HasQuotient.Quotientstatement and proof · cited by 2,301
- Ideal.IsPrimeproof · cited by 827
- Ideal.Quotient.mkproof · cited by 610
- Ideal.IsMaximalproof · cited by 452
- Ideal.comapproof · cited by 443
- IsLocalRingstatement and proof · cited by 339
Cited by1
Results whose statement or proof uses this declaration.
- Ideal.height_le_one_of_isPrincipal_of_mem_minimalPrimes_of_isLocalRingproof · cited by 1