Some properties of the construction D + DX + X2K[X]

Let [Formula: see text] be a Bézout domain with quotient field [Formula: see text], it is proved in this paper that every finitely generated ideal of the constructed polynomial domain [Formula: see text] is [Formula: see text]-projective. It is also proved that if [Formula: see text] is a Bézout domain with quotient field [Formula: see text], [Formula: see text] is an integer and [Formula: see text], then every finitely generated ideal of [Formula: see text] is [Formula: see text]-generated but [Formula: see text] is not coherent.