Abstract
The study of prime ideals has been an area of active research. In recent past a considerable work has been done in this direction. Associated prime ideals and minimal prime ideals of certain types of Ore extensions have been characterized.In this paper a relation between completely prime ideals of a ring R and those of R[x; σ, δ] has been given; σ is an automorphisms of R and δ is a σ-derivation of R. It has been proved that if P is a completely prime ideal of R such that σ(P) = P and δ(P) ⊆ P, then P[x; σ, δ] is a completely prime ideal of R[x; σ, δ]. It has also been proved that this type of relation does not hold for strongly prime ideals.
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