Theorems · Inductive type · commutative algebra
Ring.HasFiniteQuotients
(R : Type u_1) → [CommRing R] → Prop
A ring R has finite quotients if the quotient R ⧸ I is finite for all nonzero ideals of R.
- Cited by
- 19 results in Mathlib
- Foundations
- Depth 1 from the axioms · uses no axioms
- Assumes
- CommRing
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites1
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- CommRingstatement · cited by 17,173
Cited by21
Results whose statement or proof uses this declaration.
- Ring.HasFiniteQuotients.finiteQuotientstatement and proof · cited by 8
- Ring.HasFiniteQuotients.finite_cardQuot_lestatement and proof · cited by 2
- Ring.HasFiniteQuotients.finite_setOfPred_memstatement and proof · cited by 2
- IsDecompositionField.inertiaDegIn_eqstatement and proof · cited by 1
- IsInertiaField.rank_leftstatement and proof · cited by 1
- IsInertiaField.rank_rightstatement and proof · cited by 1
- IsDecompositionField.ramificationIdxIn_eqstatement and proof · cited by 1
- IsDecompositionField.rank_leftstatement and proof · cited by 1
- IsDecompositionField.rank_rightstatement and proof · cited by 1
- Ring.HasFiniteQuotients.finite_cardQuot_heightOneSpectrum_lestatement and proof · cited by 1
- IsDecompositionField.inertiaDeg_eqstatement and proof · cited by 0
- IsInertiaField.rank_decompositionFieldstatement and proof · cited by 0