Theorems · Theorem · commutative algebra
ringKrullDim_quotient_succ_le_of_nonZeroDivisor
∀ {R : Type u_1} [inst : CommRing R] {r : R},
r ∈ nonZeroDivisors R → ringKrullDim (R ⧸ Ideal.span {r}) + 1 ≤ ringKrullDim R- Cited by
- 3 results in Mathlib
- Foundations
- Depth 91 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.
Cites52
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
- Top.topproof · cited by 9,680
- SetLike.coeproof · cited by 8,199
- Set.Elemproof · cited by 7,166
- ENatstatement and proof · cited by 4,985
- Idealstatement and proof · cited by 4,748
- Bot.botproof · cited by 4,720
- Submonoidstatement · cited by 3,086
- Nat.cast_oneproof · cited by 2,501
- Nontrivialproof · cited by 2,416
- iSupproof · cited by 2,415
Cited by3
Results whose statement or proof uses this declaration.
- ringKrullDim_succ_le_of_surjectiveproof · cited by 2
- isFiniteLength_quotient_span_singletonproof · cited by 1
- Module.ringKrullDim_quotient_add_one_of_mem_nonZeroDivisorsproof · cited by 0