Theorems · Theorem · commutative algebra
Ideal.finite_quotient_pow
∀ {R : Type u_1} [inst : CommRing R] {I : Ideal R}, I.FG → ∀ [Finite (R ⧸ I)] (n : ℕ), Finite (R ⧸ I ^ n)- Defined in
- Mathlib.RingTheory.Ideal.Quotient.Index
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 101 from the axioms · uses propext, Classical.choice, Quot.sound
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.
- CommRingstatement and proof · cited by 17,173
- Idealstatement and proof · cited by 4,748
- Finitestatement and proof · cited by 3,029
- HasQuotient.Quotientstatement and proof · cited by 2,301
- pow_zeroproof · cited by 1,094
- Ideal.FGstatement and proof · cited by 99
- Ideal.one_eq_topproof · cited by 83
- Submodule.finite_quotient_smulproof · cited by 2
Cited by3
Results whose statement or proof uses this declaration.
- IsArtinianRing.finite_of_compactSpace_of_t2Spaceproof · cited by 0
- Ideal.index_pow_leproof · cited by 0
- IsLocalRing.finite_quotient_iffproof · cited by 0