Identities, Ore extensions and character skew derivations

Following [17], a σ-derivation δ is called quasi  -algebraic if there exist a,ai∈Qa,ai∈Q such that δk(x)+∑i=1k−1aiδi(x)+ax−σk(x)a=0 for x∈Qx∈Q. Let k   be the minimal such integer and g0,g1,…g0,g1,… mutually outer automorphisms of Q  . Let f(zij)f(zij) be a generalized polynomial in variables zijzij, where i≥0i≥0 and 0≤j