Theorems · Theorem · commutative algebra
TensorProduct.Algebra.exists_of_fg
∀ {R : Type u_1} {S : Type u_2} {N : Type u_4} [inst : CommSemiring R] [inst_1 : Semiring S] [inst_2 : Algebra R S]
[inst_3 : AddCommMonoid N] [inst_4 : Module R N] (u : TensorProduct R S N),
∃ A, A.FG ∧ u ∈ (LinearMap.rTensor N A.val.toLinearMap).range- Cited by
- 3 results in Mathlib
- Foundations
- Depth 100 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites30
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- Modulestatement and proof · cited by 20,661
- RingHom.idstatement and proof · cited by 18,349
- Semiringstatement and proof · cited by 13,802
- Finsetproof · cited by 13,712
- AddCommMonoidstatement and proof · cited by 12,281
- Algebrastatement and proof · cited by 11,388
- CommSemiringstatement and proof · cited by 10,911
- LinearMapproof · cited by 10,215
- SetLike.coeproof · cited by 8,199
- Submodulestatement and proof · cited by 7,192
- TensorProductstatement and proof · cited by 2,545
Cited by3
Results whose statement or proof uses this declaration.
- PolynomialLaw.π_surjectiveproof · cited by 8
- PolynomialLaw.exists_lift'proof · cited by 0
- Submodule.exists_fg_of_baseChange_eq_zeroproof · cited by 0