Theorems · Theorem · commutative algebra
exists_fg_and_mem_baseChange
∀ {R : Type u_1} {A : Type u_2} {B : Type u_3} [inst : CommSemiring R] [inst_1 : CommSemiring A] [inst_2 : Semiring B]
[inst_3 : Algebra R A] [inst_4 : Algebra R B] (x : TensorProduct R A B), ∃ C, C.FG ∧ x ∈ Subalgebra.baseChange A C- Defined in
- Mathlib.RingTheory.Adjoin.FGBaseChange
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 81 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites19
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
- 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
- Finset.sumproof · cited by 5,195
- TensorProductstatement and proof · cited by 2,545
- Subalgebrastatement · cited by 1,353
- TensorProduct.tmulproof · cited by 1,182
- Finset.imageproof · cited by 910
- Algebra.adjoinproof · cited by 535
- Algebra.subset_adjoinproof · cited by 109
Cited by2
Results whose statement or proof uses this declaration.
- IsReduced.tensorProduct_of_flat_of_forall_fgproof · cited by 1
- PrimeSpectrum.isOpenMap_comap_algebraMap_tensorProduct_of_fieldproof · cited by 0