  Let R = D[x;\sigma;\delta] be an Ore extension over a commutative Dedekind
domain D, where \sigma is an automorphism on D. In the case \delta = 0
Marubayashi et. al. already investigated the class of minimal prime ideals in
term of their contraction on the coefficient ring D. In this note we extend
this result to a general case \delta not 0.
