Theorems · Theorem · commutative algebra
Polynomial.degree_annIdealGenerator_le_of_mem
∀ {𝕜 : Type u_1} {A : Type u_2} [inst : Field 𝕜] [inst_1 : Ring A] [inst_2 : Algebra 𝕜 A] (a : A),
∀ p ∈ Polynomial.annIdeal 𝕜 a, p ≠ 0 → (Polynomial.annIdealGenerator 𝕜 a).degree ≤ p.degreeThe generator of the annihilating ideal has minimal degree among the non-zero members of the annihilating ideal
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 127 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.
- Algebrastatement and proof · cited by 11,388
- Ringstatement and proof · cited by 7,463
- Fieldstatement and proof · cited by 7,404
- Polynomialstatement and proof · cited by 5,681
- Idealstatement · cited by 4,748
- WithBotstatement · cited by 1,498
- Polynomial.degreestatement · cited by 643
- Polynomial.annIdealGeneratorstatement · cited by 10
- Polynomial.annIdealstatement and proof · cited by 8
- Polynomial.degree_le_of_dvdproof · cited by 5
- Polynomial.mem_iff_annIdealGenerator_dvdproof · cited by 1
Cited by1
Results whose statement or proof uses this declaration.
- Polynomial.annIdealGenerator_eq_minpolyproof · cited by 1