Theorems · Theorem · commutative algebra
Polynomial.isNilpotent_aeval_sub_of_isNilpotent_sub
∀ {R : Type u_2} {S : Type u_3} [inst : CommRing R] [inst_1 : CommRing S] [inst_2 : Algebra R S] (P : Polynomial R)
{a b : S}, IsNilpotent (a - b) → IsNilpotent ((Polynomial.aeval a) P - (Polynomial.aeval b) P)- Defined in
- Mathlib.RingTheory.Polynomial.Nilpotent
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 113 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites13
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement · cited by 62,936
- CommRingstatement and proof · cited by 17,173
- Algebrastatement and proof · cited by 11,388
- Polynomialstatement and proof · cited by 5,681
- Algebra.algebraMapproof · cited by 4,706
- AlgHomstatement · cited by 3,236
- Polynomial.mapproof · cited by 806
- Polynomial.evalproof · cited by 796
- Polynomial.aevalstatement · cited by 615
- IsNilpotentstatement and proof · cited by 248
- Commute.allproof · cited by 119
- Commute.isNilpotent_mul_leftproof · cited by 7
Cited by2
Results whose statement or proof uses this declaration.
- Polynomial.isUnit_aeval_of_isUnit_aeval_of_isNilpotent_subproof · cited by 2
- Polynomial.isNilpotent_iterate_newtonMap_sub_of_isNilpotentproof · cited by 2