Theorems · Theorem · commutative algebra
isNoetherianRing_of_fg
∀ {R : Type u} {A : Type v} [inst : CommRing R] [inst_1 : CommRing A] [inst_2 : Algebra R A] {S : Subalgebra R A},
S.FG → ∀ [IsNoetherianRing R], IsNoetherianRing ↥S- Defined in
- Mathlib.RingTheory.Adjoin.FG
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 116 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites10
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
- Finsetproof · cited by 13,712
- Algebrastatement and proof · cited by 11,388
- SetLike.coeproof · cited by 8,199
- Subalgebrastatement and proof · cited by 1,353
- Algebra.adjoinproof · cited by 535
- MvPolynomial.aevalproof · cited by 298
- IsNoetherianRingstatement and proof · cited by 268
- Subalgebra.FGstatement and proof · cited by 45
- Algebra.adjoin_eq_rangeproof · cited by 3
Cited by2
Results whose statement or proof uses this declaration.
- fg_of_fg_of_fgproof · cited by 0
- is_noetherian_subring_closureproof · cited by 0