Theorems · Theorem · commutative algebra
MonoidAlgebra.support_gen_of_gen
∀ {R : Type u_1} {M : Type u_2} [inst : CommSemiring R] [inst_1 : Monoid M] {S : Set (MonoidAlgebra R M)},
Algebra.adjoin R S = ⊤ → Algebra.adjoin R (⋃ f ∈ S, ⇑(MonoidAlgebra.of R M) '' ↑f.coeff.support) = ⊤If a set S generates, as algebra, R[M], then the set of supports of elements
of S generates R[M].
- Defined in
- Mathlib.RingTheory.FiniteType
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 86 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- CommSemiringMonoid
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites22
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement and proof · cited by 62,936
- Setstatement and proof · cited by 53,352
- Finsetstatement · cited by 13,712
- CommSemiringstatement and proof · cited by 10,911
- Top.topstatement and proof · cited by 9,680
- SetLike.coestatement and proof · cited by 8,199
- Set.imagestatement and proof · cited by 5,609
- Monoidstatement and proof · cited by 3,887
- MonoidHomstatement · cited by 3,629
- Set.iUnionstatement and proof · cited by 2,483
- le_antisymmproof · cited by 2,068
- Subalgebrastatement and proof · cited by 1,353
Cited by1
Results whose statement or proof uses this declaration.
- MonoidAlgebra.support_gen_of_gen'proof · cited by 1