Theorems · Theorem · commutative algebra
Module.supportDim_self_eq_ringKrullDim
∀ (R : Type u_1) [inst : CommRing R], Module.supportDim R R = ringKrullDim R
- 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.
Cites16
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- CommRingstatement and proof · cited by 17,173
- ENatstatement and proof · cited by 4,985
- Idealproof · cited by 4,748
- Bot.botproof · cited by 4,720
- Algebra.algebraMapproof · cited by 4,706
- HasQuotient.Quotientproof · cited by 2,301
- WithBotstatement and proof · cited by 1,498
- ringKrullDimstatement and proof · cited by 75
- Module.annihilatorproof · cited by 61
- Module.supportDimstatement · cited by 23
- faithfulSMul_iff_algebraMap_injectiveproof · cited by 17
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