Theorems · Theorem · commutative algebra
Ideal.height_bot
∀ {R : Type u_1} [inst : CommRing R] [Nontrivial R], ⊥.height = 0- Defined in
- Mathlib.RingTheory.Ideal.Height
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 77 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- CommRingNontrivial
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites12
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
- Set.Elemproof · cited by 7,166
- ENatstatement and proof · cited by 4,985
- Idealstatement and proof · cited by 4,748
- Bot.botstatement and proof · cited by 4,720
- Nontrivialstatement and proof · cited by 2,416
- Ideal.heightstatement · cited by 83
- Ideal.minimalPrimesproof · cited by 74
- top_ne_botproof · cited by 15
- Ideal.height_eq_inf_minimalPrimesproof · cited by 7
- Ideal.nonempty_minimalPrimesproof · cited by 7
- Ideal.height_eq_zero_iffproof · cited by 5
Cited by4
Results whose statement or proof uses this declaration.
- Ideal.height_eq_zero_iff_eq_botproof · cited by 2
- Polynomial.height_map_Cproof · cited by 1
- Ideal.sup_isPrime_height_eq_ringKrullDimproof · cited by 0
- IsPrincipalIdealRing.height_eq_one_of_isMaximalproof · cited by 0