Theorems · Theorem · commutative algebra
Subalgebra.FG.map
∀ {R : Type u} {A : Type v} {B : Type w} [inst : CommSemiring R] [inst_1 : Semiring A] [inst_2 : Algebra R A]
[inst_3 : Semiring B] [inst_4 : Algebra R B] {S : Subalgebra R A} (f : A →ₐ[R] B), S.FG → (Subalgebra.map f S).FG- Defined in
- Mathlib.RingTheory.Adjoin.FG
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 77 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites15
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- Setproof · cited by 53,352
- Semiringstatement and proof · cited by 13,802
- Finsetproof · cited by 13,712
- Algebrastatement and proof · cited by 11,388
- CommSemiringstatement and proof · cited by 10,911
- SetLike.coeproof · cited by 8,199
- AlgHomstatement and proof · cited by 3,236
- Subalgebrastatement and proof · cited by 1,353
- Finset.imageproof · cited by 910
- Algebra.adjoinproof · cited by 535
- Finset.coe_imageproof · cited by 222
Cited by3
Results whose statement or proof uses this declaration.
- Algebra.FiniteType.of_surjectiveproof · cited by 11
- Subalgebra.fg_topproof · cited by 4
- PolynomialLaw.factorsThrough_toFunLifted_πproof · cited by 1