Theorems · Theorem · commutative algebra
Algebra.FiniteType.out
∀ {R : Type uR} {A : Type uA} {inst : CommSemiring R} {inst_1 : Semiring A} {inst_2 : Algebra R A}
[self : Algebra.FiniteType R A], ⊤.FG- Defined in
- Mathlib.RingTheory.FiniteType
- Cited by
- 14 results in Mathlib
- Foundations
- Depth 75 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- Algebra.FiniteType
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.
- Semiringstatement and proof · cited by 13,802
- Algebrastatement and proof · cited by 11,388
- CommSemiringstatement and proof · cited by 10,911
- Top.topstatement · cited by 9,680
- Subalgebrastatement · cited by 1,353
- Algebra.FiniteTypestatement and proof · cited by 84
- Subalgebra.FGstatement · cited by 45
Cited by14
Results whose statement or proof uses this declaration.
- Algebra.FiniteType.of_surjectiveproof · cited by 11
- Algebra.FiniteType.isNoetherianRingproof · cited by 6
- Algebra.FiniteType.of_restrictScalars_finiteTypeproof · cited by 3
- Algebra.FiniteType.transproof · cited by 3
- Algebra.FiniteType.of_finiteType_tensorProduct_of_faithfullyFlatproof · cited by 3
- Algebra.FiniteType.of_span_eq_top_targetproof · cited by 2
- Subalgebra.fg_iff_finiteTypeproof · cited by 2
- Algebra.FinitePresentation.of_restrict_scalars_finitePresentationproof · cited by 2
- Localization.exists_awayMap_bijective_of_localRingHom_bijectiveproof · cited by 1
- PolynomialLaw.factorsThrough_toFunLifted_πproof · cited by 1
- GradedAlgebra.exists_finset_adjoin_eq_top_and_homogeneousproof · cited by 1