chore(ring_theory/adjoin_root): modify field instance on `adjoin_ro…

…ot` (#19119)

We copy the fields of `group_with_zero` instead of `field`.  This speeds up the already ported `adjoin_root/AdjoinRoot` pair.

[Zulip discussion](https://leanprover.zulipchat.com/#narrow/stream/287929-mathlib4/topic/!4.234339.20.20FieldTheory.2ESplittingField)

src/ring_theory/adjoin_root.lean

@@ -322,7 +322,7 @@ noncomputable instance field [fact (irreducible f)] : field (adjoin_root f) :=
   qsmul_eq_mul' := λ a x, adjoin_root.induction_on _ x (λ p,
     by { rw [smul_mk, of, ring_hom.comp_apply, ← (mk f).map_mul, polynomial.rat_smul_eq_C_mul] }),
   ..adjoin_root.comm_ring f,
-  ..ideal.quotient.field (span {f} : ideal K[X]) }
+  ..ideal.quotient.group_with_zero (span {f} : ideal K[X]) }
 
 lemma coe_injective (h : degree f ≠ 0) : function.injective (coe : K → adjoin_root f) :=
 have _ := adjoin_root.nontrivial f h, by exactI (of f).injective