Mathlib Map

Theorems · Definition · commutative algebra

IsAdjoinRoot.map

{R : Type u} →
  {S : Type v} →
    [inst : CommSemiring R] →
      [inst_1 : Semiring S] → [inst_2 : Algebra R S] → {f : Polynomial R} → IsAdjoinRoot S f → Polynomial R →ₐ[R] S
Defined in
Mathlib.RingTheory.IsAdjoinRoot
Cited by
32 results in Mathlib
Foundations
Depth 105 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
CommSemiringSemiringAlgebra
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Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

IsAdjoinRoot.root · cited by 34IsAdjoinRoot.rootIsAdjoinRootMonic.basis · cited by 10IsAdjoinRootMonic.basisIsAdjoinRoot.map_repr · cited by 9IsAdjoinRoot.map_reprIsAdjoinRoot.aeval_root_eq_map · cited by 5IsAdjoinRoot.aeval_root_e…IsAdjoinRoot.lift_map · cited by 5IsAdjoinRoot.lift_mapIsAdjoinRoot.ofAlgEquiv · cited by 4IsAdjoinRoot.ofAlgEquivIsAdjoinRoot.ker_map · cited by 3IsAdjoinRoot.ker_mapIsAdjoinRoot.mem_ker_map · cited by 3IsAdjoinRoot.mem_ker_mapIsAdjoinRootMonic.modByMonicHom_root_pow · cited by 2IsAdjoinRootMonic.modByMo…IsAdjoinRoot.adjoinRootAlgEquiv_apply_eq_map · cited by 2IsAdjoinRoot.adjoinRootAl…IsAdjoinRoot.adjoinRootAlgEquiv_apply_mk · cited by 2IsAdjoinRoot.adjoinRootAl…IsAdjoinRoot.algebraMap_apply · cited by 2IsAdjoinRoot.algebraMap_a…IsAdjoinRoot.apply_eq_lift · cited by 2IsAdjoinRoot.apply_eq_liftIsAdjoinRoot.map_X · cited by 2IsAdjoinRoot.map_XIsAdjoinRoot.map_self · cited by 2IsAdjoinRoot.map_selfSemiring · cited by 13802SemiringAlgebra · cited by 11388AlgebraCommSemiring · cited by 10911CommSemiringPolynomial · cited by 5681PolynomialAlgHom · cited by 3236AlgHomIsAdjoinRoot · cited by 61IsAdjoinRootIsAdjoinRoot.mapCITED BYCITES

Cites6

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Cited by35

Results whose statement or proof uses this declaration.