Theorems · Theorem · commutative algebra
Ideal.map_height_le_one_of_mem_minimalPrimes
∀ {R : Type u_1} [inst : CommRing R] [IsNoetherianRing R] {I p : Ideal R} {x : R},
p ∈ (I ⊔ Ideal.span {x}).minimalPrimes → (Ideal.map (Ideal.Quotient.mk I) p).height ≤ 1- Cited by
- 1 results in Mathlib
- Foundations
- Depth 138 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- CommRingIsNoetherianRing
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites34
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement · cited by 53,352
- CommRingstatement and proof · cited by 17,173
- RingHomstatement and proof · cited by 10,189
- ENatstatement · cited by 4,985
- Idealstatement and proof · cited by 4,748
- LE.le.transproof · cited by 3,151
- HasQuotient.Quotientstatement and proof · cited by 2,301
- Ideal.spanstatement and proof · cited by 948
- Ideal.IsPrimeproof · cited by 827
- Ideal.mapstatement and proof · cited by 692
- Ideal.Quotient.mkstatement and proof · cited by 610
- Eq.leproof · cited by 605
Cited by1
Results whose statement or proof uses this declaration.
- PrimeSpectrum.exist_mem_one_of_mem_maximal_idealproof · cited by 1