Sets of lengths in V+XB[X] domains

In this paper, we investigate factorization properties in domains of type V + XB[X], where B is the integral closure of V in a finite algebraic extens ion of the quotient field of V. We place particular emphasis on the case wh ere V is a discrete valuation ring in which the unique up to associate irre ducible element p of V ramifies in B. More precisely, we compute in this ca se the sets of lengths of the elements of V + XB [X] and, in some cases, th e generalized sets of lengths.