Theorems · Theorem · commutative algebra
Algebra.adjoin_range_eq_range_aeval
∀ (R : Type u) {S₁ : Type v} {σ : Type u_1} [inst : CommSemiring R] [inst_1 : CommSemiring S₁] [inst_2 : Algebra R S₁]
(f : σ → S₁), Algebra.adjoin R (Set.range f) = (MvPolynomial.aeval f).range- Defined in
- Mathlib.Algebra.MvPolynomial.Eval
- Cited by
- 6 results in Mathlib
- Foundations
- Depth 96 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites14
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- Algebrastatement and proof · cited by 11,388
- CommSemiringstatement and proof · cited by 10,911
- Finsuppstatement · cited by 5,255
- Set.rangestatement and proof · cited by 4,705
- MvPolynomialstatement · cited by 2,140
- Subalgebrastatement · cited by 1,353
- MvPolynomial.Xproof · cited by 552
- Algebra.adjoinstatement and proof · cited by 535
- MvPolynomial.aevalstatement and proof · cited by 298
- AlgHom.rangestatement · cited by 169
- MvPolynomial.aeval_Xproof · cited by 105
Cited by6
Results whose statement or proof uses this declaration.
- Algebra.FiniteType.isNoetherianRingproof · cited by 6
- MvPolynomial.supported_eq_range_renameproof · cited by 5
- PolynomialLaw.range_φproof · cited by 3
- Algebra.adjoin_eq_rangeproof · cited by 3
- Algebra.FinitePresentation.of_restrict_scalars_finitePresentationproof · cited by 2
- IntermediateField.mem_adjoin_range_iffproof · cited by 1