Theorems · Theorem · commutative algebra
IsLocalRing.exists_maximalIdeal_pow_le_of_isArtinianRing_quotient
∀ {R : Type u_1} [inst : CommRing R] [inst_1 : IsLocalRing R] (I : Ideal R) [IsArtinianRing (R ⧸ I)],
∃ n, IsLocalRing.maximalIdeal R ^ n ≤ I- Defined in
- Mathlib.RingTheory.LocalRing.Quotient
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 99 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites29
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- CommRingstatement and proof · cited by 17,173
- Top.topproof · cited by 9,680
- Idealstatement and proof · cited by 4,748
- Bot.botproof · cited by 4,720
- Nontrivialproof · cited by 2,416
- HasQuotient.Quotientstatement and proof · cited by 2,301
- IsUnitproof · cited by 1,602
- Ideal.mapproof · cited by 692
- Ideal.Quotient.mkproof · cited by 610
- IsLocalRingstatement and proof · cited by 339
- IsLocalRing.maximalIdealstatement and proof · cited by 297
Cited by2
Results whose statement or proof uses this declaration.
- IsLocalRing.finite_quotient_iffproof · cited by 0
- IsLocalRing.isOpen_iff_finite_quotientproof · cited by 0