Theorems · Theorem · commutative algebra
ringKrullDim_le_ringKrullDim_quotient_add_spanFinrank
∀ {R : Type u_1} [inst : CommRing R] [IsNoetherianRing R],
∀ I ≤ Ring.jacobson R, ringKrullDim R ≤ ringKrullDim (R ⧸ I) + ↑(Submodule.spanFinrank I)- Cited by
- 2 results in Mathlib
- Foundations
- Depth 148 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.
Cites20
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- CommRingstatement and proof · cited by 17,173
- ENatstatement and proof · cited by 4,985
- Idealstatement and proof · cited by 4,748
- Bot.botproof · cited by 4,720
- add_zeroproof · cited by 2,707
- Nontrivialproof · cited by 2,416
- HasQuotient.Quotientstatement and proof · cited by 2,301
- WithBotstatement and proof · cited by 1,498
- le_transproof · cited by 985
- Ideal.IsMaximalproof · cited by 452
- CharP.cast_eq_zeroproof · cited by 357
- IsNoetherianRingstatement and proof · cited by 268
Cited by2
Results whose statement or proof uses this declaration.
- ringKrullDim_le_ringKrullDim_quotient_add_encardproof · cited by 1
- ringKrullDim_le_ringKrullDim_add_spanFinrankproof · cited by 0