Theorems · Theorem · commutative algebra
IsLocalRing.isMaximal_iff
∀ (R : Type u_1) [inst : CommSemiring R] [inst_1 : IsLocalRing R] {I : Ideal R},
I.IsMaximal ↔ I = IsLocalRing.maximalIdeal R- Cited by
- 3 results in Mathlib
- Foundations
- Depth 31 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.
Cites8
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 and proof · cited by 452
- IsLocalRingstatement and proof · cited by 339
- IsLocalRing.maximalIdealstatement and proof · cited by 297
- Ideal.IsMaximal.eq_of_leproof · cited by 39
- Ideal.eq_top_of_isUnit_memproof · cited by 26
- Ideal.IsMaximal.outproof · cited by 16
Cited by3
Results whose statement or proof uses this declaration.
- Ideal.ramificationIdx_eq_one_iffproof · cited by 4
- Ideal.ramificationIdx_eq_oneproof · cited by 3
- isArtinianRing_iff_isNilpotent_maximalIdealproof · cited by 1