Theorems · Theorem · commutative algebra
Subalgebra.fg_of_noetherian
∀ {R : Type u} {A : Type v} [inst : CommSemiring R] [inst_1 : Semiring A] [inst_2 : Algebra R A] [IsNoetherian R A]
(S : Subalgebra R A), S.FG- Defined in
- Mathlib.RingTheory.Adjoin.FG
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 72 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.
- DFunLike.coeproof · cited by 62,936
- Semiringstatement and proof · cited by 13,802
- Algebrastatement and proof · cited by 11,388
- CommSemiringstatement and proof · cited by 10,911
- Subalgebrastatement and proof · cited by 1,353
- IsNoetherianstatement and proof · cited by 208
- Subalgebra.toSubmoduleproof · cited by 141
- Subalgebra.FGstatement · cited by 45
- IsNoetherian.noetherianproof · cited by 32
- Subalgebra.fg_of_fg_toSubmoduleproof · cited by 1
Cited by2
Results whose statement or proof uses this declaration.
- IntermediateField.fg_of_noetherianproof · cited by 1
- Subalgebra.induction_on_adjoinproof · cited by 0