Theorems · Theorem · commutative algebra
Polynomial.exists_dvd_map_of_isAlgebraic
∀ {R : Type u_1} {S : Type u_2} [inst : CommRing R] [inst_1 : CommRing S] [inst_2 : Algebra R S]
[alg : Algebra.IsAlgebraic R S] [NoZeroDivisors S] {f : Polynomial S},
f ≠ 0 → ∃ g, g ≠ 0 ∧ f ∣ Polynomial.map (algebraMap R S) g- Defined in
- Mathlib.RingTheory.Algebraic.Integral
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 140 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites10
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- CommRingstatement and proof · cited by 17,173
- Algebrastatement and proof · cited by 11,388
- Polynomialstatement and proof · cited by 5,681
- Algebra.algebraMapstatement · cited by 4,706
- Polynomial.mapstatement · cited by 806
- NoZeroDivisorsstatement and proof · cited by 545
- Algebra.IsAlgebraicstatement and proof · cited by 322
- Algebra.IsAlgebraic.isAlgebraicproof · cited by 51
- mem_nonZeroDivisors_of_ne_zeroproof · cited by 34
- IsAlgebraic.exists_nonzero_dvdproof · cited by 5
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