Sets of lengths in V +XB [X] domains

الملخص EN

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 extension of the quotient field of V.

We place particular emphasis on the case where V is a discrete valuation ring in which the unique up to associate irreducible element p of V ramifies in B.

More precisely, we compute in this case the sets of lengths of the elements of V + XB[X] and, in some cases, the generalized sets of lengths.