Theorems · Theorem · commutative algebra
Subalgebra.fg_top
∀ {R : Type u} {A : Type v} [inst : CommSemiring R] [inst_1 : Semiring A] [inst_2 : Algebra R A] (S : Subalgebra R A),
⊤.FG ↔ S.FG- Defined in
- Mathlib.RingTheory.Adjoin.FG
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 78 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- CommSemiringSemiringAlgebra
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites12
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Semiringstatement and proof · cited by 13,802
- Algebrastatement and proof · cited by 11,388
- CommSemiringstatement and proof · cited by 10,911
- Top.topstatement and proof · cited by 9,680
- Subalgebrastatement and proof · cited by 1,353
- Subtype.val_injectiveproof · cited by 232
- Subalgebra.valproof · cited by 104
- Subalgebra.FGstatement and proof · cited by 45
- Algebra.map_topproof · cited by 27
- Subalgebra.range_valproof · cited by 9
- Subalgebra.FG.mapproof · cited by 3
- Subalgebra.fg_of_fg_mapproof · cited by 1
Cited by4
Results whose statement or proof uses this declaration.
- Subalgebra.fg_iff_finiteTypeproof · cited by 2
- fg_of_fg_of_fgproof · cited by 0
- PrimeSpectrum.isOpenMap_comap_algebraMap_tensorProduct_of_fieldproof · cited by 0
- Algebra.Smooth.exists_finiteTypeproof · cited by 0