Theorems · Theorem · commutative algebra
IsLocalRing.maximal_ideal_unique
∀ (R : Type u_1) [inst : CommSemiring R] [IsLocalRing R], ∃! I, I.IsMaximal
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 33 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- CommSemiringIsLocalRing
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites5
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- CommSemiringstatement and proof · cited by 10,911
- Idealstatement and proof · cited by 4,748
- Ideal.IsMaximalstatement · cited by 452
- IsLocalRingstatement and proof · cited by 339
- ExistsUniquestatement and proof · cited by 268
Cited by2
Results whose statement or proof uses this declaration.
- IsLocalRing.eq_maximalIdealproof · cited by 20
- IsLocalHom.of_surjectiveproof · cited by 4