Theorems · Theorem · commutative algebra
IsArtinianRing.setOfPred_isMaximal_finite
∀ (R : Type u_1) [inst : CommSemiring R] [IsArtinianRing R], {I | I.IsMaximal}.Finite[Stacks Tag 00J7](https://stacks.math.columbia.edu/tag/00J7)
- Defined in
- Mathlib.RingTheory.Artinian.Module
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 83 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- CommSemiringIsArtinianRing
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites15
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Finsetproof · cited by 13,712
- CommSemiringstatement and proof · cited by 10,911
- Set.Elemproof · cited by 7,166
- Set.ofPredstatement and proof · cited by 6,101
- Idealstatement and proof · cited by 4,748
- Set.Finitestatement and proof · cited by 1,814
- Ideal.IsMaximalstatement and proof · cited by 452
- Finset.infproof · cited by 219
- IsArtinianRingstatement and proof · cited by 98
- Ideal.IsMaximal.isPrimeproof · cited by 53
- Ideal.IsMaximal.ne_topproof · cited by 42
- Ideal.IsMaximal.eq_of_leproof · cited by 39
Cited by2
Results whose statement or proof uses this declaration.
- IsArtinianRing.setOfPred_isPrime_finiteproof · cited by 1
- IsArtinianRing.setOf_isMaximal_finiteproof · cited by 0