Theorems · Theorem · commutative algebra
Ideal.height_le_one_of_isPrincipal_of_mem_minimalPrimes_of_isLocalRing
∀ {R : Type u_1} [inst : CommRing R] [IsNoetherianRing R] [inst_2 : IsLocalRing R] (I : Ideal R)
[Submodule.IsPrincipal I], IsLocalRing.maximalIdeal R ∈ I.minimalPrimes → (IsLocalRing.maximalIdeal R).height ≤ 1- Cited by
- 1 results in Mathlib
- Foundations
- Depth 136 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites81
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- Setstatement · cited by 53,352
- CommRingstatement and proof · cited by 17,173
- RingHomproof · cited by 10,189
- Ringproof · cited by 7,463
- ENatstatement and proof · cited by 4,985
- Idealstatement and proof · cited by 4,748
- Bot.botproof · cited by 4,720
- Algebra.algebraMapproof · cited by 4,706
- HasQuotient.Quotientproof · cited by 2,301
- mul_commproof · cited by 2,262
- LT.lt.leproof · cited by 2,189
Cited by1
Results whose statement or proof uses this declaration.
- Ideal.height_le_one_of_isPrincipal_of_mem_minimalPrimesproof · cited by 4