Theorems · Theorem · commutative algebra
Module.supportDim_quotient_eq_ringKrullDim
∀ {R : Type u_1} [inst : CommRing R] (I : Ideal R), Module.supportDim R (R ⧸ I) = ringKrullDim (R ⧸ I)- Defined in
- Mathlib.RingTheory.KrullDimension.Module
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 90 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.
Cites9
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
- HasQuotient.Quotientstatement and proof · cited by 2,301
- WithBotstatement and proof · cited by 1,498
- ringKrullDimstatement and proof · cited by 75
- Module.supportDimstatement · cited by 23
- Ideal.annihilator_quotientproof · cited by 4
- Module.supportDim_eq_ringKrullDim_quotient_annihilatorproof · cited by 2
Cited by3
Results whose statement or proof uses this declaration.
- ringKrullDim_quotSMulTop_succ_eq_ringKrullDim_of_mem_jacobsonproof · cited by 2
- ringKrullDim_le_ringKrullDim_quotSMulTop_succproof · cited by 0
- ringKrullDim_add_length_eq_ringKrullDim_of_isRegularproof · cited by 0