Theorems · Theorem · commutative algebra
MonoidAlgebra.fg_of_finiteType
∀ {R : Type u_1} {M : Type u_2} [inst : Monoid M] [inst_1 : CommRing R] [Nontrivial R]
[h : Algebra.FiniteType R (MonoidAlgebra R M)], Monoid.FG MIf R[M] is of finite type then M is finitely generated.
- Defined in
- Mathlib.RingTheory.FiniteType
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 91 from the axioms · uses propext, Classical.choice, Quot.sound
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
- Monoidstatement and proof · cited by 3,887
- Nontrivialstatement and proof · cited by 2,416
- MonoidAlgebrastatement and proof · cited by 590
- Algebra.FiniteTypestatement and proof · cited by 84
- Monoid.FGstatement · cited by 19
- MonoidAlgebra.finiteType_iff_fgproof · cited by 2
Cited by0
Results whose statement or proof uses this declaration.
Nothing cites this yet.