Theorems · Theorem · commutative algebra
IsAdjoinRoot.map_repr
∀ {R : Type u} {S : Type v} [inst : CommRing R] [inst_1 : Ring S] {f : Polynomial R} [inst_2 : Algebra R S]
(h : IsAdjoinRoot S f) (x : S), h.map (h.repr x) = x- Defined in
- Mathlib.RingTheory.IsAdjoinRoot
- Cited by
- 9 results in Mathlib
- Foundations
- Depth 109 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites10
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
- Ringstatement and proof · cited by 7,463
- Polynomialstatement and proof · cited by 5,681
- AlgHomstatement · cited by 3,236
- IsAdjoinRootstatement and proof · cited by 61
- IsAdjoinRoot.mapstatement · cited by 32
- IsAdjoinRoot.reprstatement · cited by 11
- IsAdjoinRoot.map_surjectiveproof · cited by 2
Cited by9
Results whose statement or proof uses this declaration.
- IsAdjoinRoot.apply_eq_liftproof · cited by 2
- IsAdjoinRootMonic.modByMonic_repr_mapproof · cited by 1
- IsAdjoinRoot.eval₂_repr_eq_eval₂_of_map_eqproof · cited by 1
- IsAdjoinRoot.lift_algEquivproof · cited by 1
- IsAdjoinRoot.lift_self_applyproof · cited by 1
- IsAdjoinRootMonic.map_modByMonicHomproof · cited by 0
- IsAdjoinRoot.repr_add_sub_repr_add_repr_mem_spanproof · cited by 0
- IsAdjoinRoot.adjoinRootAlgEquiv_symm_apply_eq_mkproof · cited by 0
- IsAdjoinRoot.repr_zero_mem_spanproof · cited by 0