Theorems · Theorem · commutative algebra
Algebra.Presentation.HasCoeffs.coeffs_relation_mem_range
∀ {R : Type u_1} {S : Type u_2} {ι : Type u_3} {σ : Type u_4} [inst : CommRing R] [inst_1 : CommRing S]
[inst_2 : Algebra R S] {P : Algebra.Presentation R S ι σ} (R₀ : Type u_5) [inst_3 : CommRing R₀]
[inst_4 : Algebra R₀ R] [inst_5 : Algebra R₀ S] [inst_6 : IsScalarTower R₀ R S] [P.HasCoeffs R₀] (x : σ),
↑(MvPolynomial.coeffs (P.relation x)) ⊆ Set.range ⇑(algebraMap R₀ R)- Cited by
- 1 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.
Cites17
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement · cited by 62,936
- Setstatement · cited by 53,352
- CommRingstatement and proof · cited by 17,173
- Finsetstatement · cited by 13,712
- Algebrastatement and proof · cited by 11,388
- RingHomstatement · cited by 10,189
- SetLike.coestatement · cited by 8,199
- Algebra.algebraMapstatement · cited by 4,706
- Set.rangestatement · cited by 4,705
- IsScalarTowerstatement and proof · cited by 3,896
- Algebra.Presentationstatement and proof · cited by 70
- subset_transproof · cited by 63
Cited by1
Results whose statement or proof uses this declaration.
- Algebra.Presentation.HasCoeffs.relation_mem_range_mapproof · cited by 1