Algebras of constants for some extensions of derivations

AbstractLet A = B[t] be the polynomial ring in one variable over a unique factorization domain B, where k is a field of characteristic zero. Let δ be a derivation of B, ϕ ϵ B with δ(ϕ) ≠ 0, and let s be a positive integer. Denote by d the derivation of A such that d(b) = tsδ(b) for b ϵ B and d(t) = 1s+1 δ(ϕ). We describe the rings of constants of d. Several applications of our description are also given