Theorems · Theorem · commutative algebra
Algebra.adjoin_eq_range
∀ (R : Type u) {S₁ : Type v} [inst : CommSemiring R] [inst_1 : CommSemiring S₁] [inst_2 : Algebra R S₁] (s : Set S₁),
Algebra.adjoin R s = (MvPolynomial.aeval Subtype.val).range- Defined in
- Mathlib.Algebra.MvPolynomial.Eval
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 97 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites11
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement and proof · cited by 53,352
- Algebrastatement and proof · cited by 11,388
- CommSemiringstatement and proof · cited by 10,911
- Finsuppstatement · cited by 5,255
- MvPolynomialstatement · cited by 2,140
- Subalgebrastatement and proof · cited by 1,353
- Algebra.adjoinstatement and proof · cited by 535
- MvPolynomial.aevalstatement · cited by 298
- AlgHom.rangestatement · cited by 169
- Subtype.range_coeproof · cited by 98
- Algebra.adjoin_range_eq_range_aevalproof · cited by 6
Cited by3
Results whose statement or proof uses this declaration.
- AlgebraicIndependent.mapproof · cited by 3
- isNoetherianRing_of_fgproof · cited by 2
- Algebra.FiniteType.iff_quotient_mvPolynomialproof · cited by 1