Theorems · Theorem · commutative algebra
Algebra.adjoin_eq_exists_aeval
∀ (R : Type u) {A : Type z} [inst : CommSemiring R] [inst_1 : Semiring A] [inst_2 : Algebra R A] (x : A) (a : ↥R[x]),
∃ p, (Polynomial.aeval x) p = ↑a- Cited by
- 4 results in Mathlib
- Foundations
- Depth 112 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- CommSemiringSemiringAlgebra
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites12
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement and proof · cited by 62,936
- Setstatement · cited by 53,352
- Semiringstatement and proof · cited by 13,802
- Algebrastatement and proof · cited by 11,388
- CommSemiringstatement and proof · cited by 10,911
- Polynomialstatement and proof · cited by 5,681
- AlgHomstatement · cited by 3,236
- Subalgebrastatement and proof · cited by 1,353
- Polynomial.aevalstatement and proof · cited by 615
- Algebra.adjoinstatement and proof · cited by 535
- AlgHom.rangeproof · cited by 169
- Algebra.adjoin_singleton_eq_range_aevalproof · cited by 12
Cited by4
Results whose statement or proof uses this declaration.
- Algebra.exists_aeval_invOf_eq_zero_of_idealMap_adjoin_sup_span_eq_topproof · cited by 3
- Algebra.RingHom.adjoinAlgebraMap_surjectiveproof · cited by 1
- Algebra.mem_ideal_map_adjoinproof · cited by 1
- Algebra.adjoin_singleton_inductionproof · cited by 0