Completely Prime Ideals of Skew-Laurent Rings

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 the skew-Laurent ring R[x, x(-1); sigma] has been given; sigma is an automorphisms of R. It has been proved that if P is a completely prime ideal of R such that sigma(P) = P, then P[x, x(-1); sigma] is a completely prime ideal of R[x, x(-1); sigma]. It has also been proved that this type of relation does not hold for strongly prime ideals. We also discuss rings and their extensions having all prime ideals (minimal prime ideals) completely prime.