Theorems · Theorem · commutative algebra
IsArtinianRing.setOfPred_isPrime_finite
∀ (R : Type u_1) [inst : CommRing R] [IsArtinianRing R], {I | I.IsPrime}.Finite- Defined in
- Mathlib.RingTheory.Artinian.Module
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 90 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- CommRingIsArtinianRing
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.
- CommRingstatement and proof · cited by 17,173
- Set.ofPredstatement and proof · cited by 6,101
- Idealstatement and proof · cited by 4,748
- Set.Finitestatement and proof · cited by 1,814
- Ideal.IsPrimestatement · cited by 827
- IsArtinianRingstatement and proof · cited by 98
- IsArtinianRing.setOfPred_isMaximal_finiteproof · cited by 2
Cited by1
Results whose statement or proof uses this declaration.
- IsArtinianRing.setOf_isPrime_finiteproof · cited by 0