On skew polynomial rings

Abstract

In this note we consider the links of prime ideals of certain skew polynomial rings and prove our main theorem, namely theorem [5], which states the following.Let R be a noetherian ring that is link k-symmetric and let {\sigma} be an automorphism of R.Let S(R) denote the skew polynomial ring R[x,{\sigma}]. Let B be a prime ideal of S(R) that is extended from R. Then, for a prime ideal D of S(R),there is a link D\rightarrowB in the ring S(R) implies that D is an extended prime ideal of S(R).