Theorems · Theorem · commutative algebra
IsDomain.minimalPrimes_eq_singleton_bot
∀ (R : Type u_1) [inst : CommSemiring R] [IsDomain R], minimalPrimes R = {⊥}- Cited by
- 1 results in Mathlib
- Foundations
- Depth 28 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- CommSemiringIsDomain
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement · cited by 53,352
- CommSemiringstatement and proof · cited by 10,911
- Idealstatement · cited by 4,748
- Bot.botstatement · cited by 4,720
- IsDomainstatement and proof · cited by 2,196
- minimalPrimesstatement · cited by 32
- Ideal.minimalPrimes_eq_subsingleton_selfproof · cited by 3
Cited by1
Results whose statement or proof uses this declaration.
- Ideal.height_eq_zero_iff_eq_botproof · cited by 2