The construction D + DX + DX2 + ⋯ + DXk + Xk+1K[X

Abstract

Let [Formula: see text] be a [Formula: see text]-Dedekind domain with quotient field [Formula: see text] and [Formula: see text] be a fixed positive integer, it is proved in this paper that the constructed polynomial domain [Formula: see text] is a [Formula: see text]-Prüfer domain. It is also proved that if [Formula: see text] is a principal ideal domain and [Formula: see text], then every maximal ideal of [Formula: see text] is [Formula: see text]-projective.