Theorems · Theorem · commutative algebra
AddMonoidAlgebra.exists_finset_adjoin_eq_top
∀ {R : Type u_1} {M : Type u_2} [inst : CommRing R] [inst_1 : AddMonoid M]
[h : Algebra.FiniteType R (AddMonoidAlgebra R M)], ∃ G, Algebra.adjoin R (AddMonoidAlgebra.of' R M '' ↑G) = ⊤If R[M] is of finite type, then there is a G : Finset M such that its
image generates, as algebra, R[M].
- Defined in
- Mathlib.RingTheory.FiniteType
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 88 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites21
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setproof · cited by 53,352
- CommRingstatement and proof · cited by 17,173
- Finsetstatement and proof · cited by 13,712
- Top.topstatement and proof · cited by 9,680
- SetLike.coestatement and proof · cited by 8,199
- Set.imagestatement and proof · cited by 5,609
- AddMonoidstatement and proof · cited by 2,864
- Set.iUnionproof · cited by 2,483
- Subalgebrastatement · cited by 1,353
- Finsupp.supportproof · cited by 828
- AddMonoidAlgebrastatement and proof · cited by 649
- Algebra.adjoinstatement and proof · cited by 535
Cited by1
Results whose statement or proof uses this declaration.
- AddMonoidAlgebra.finiteType_iff_fgproof · cited by 3