Uniserial rings and skew polynomial rings (Q798407)

If \(\tau\) is an automorphism of a division ring D then, for each positive integer c, the factor ring \(S/x^ cS\) of the skew polynomial ring \(S=D[x;\tau]\) is a local uniserial ring of split type. The purpose of this paper is to establish a necessary and sufficient condition on a local uniserial ring R for R to be isomorphic to a ring of the above form \(S/x^ cS\), thereby generalizing a result of \textit{E. A. Behrens} [Math. Z. 77, 207-218 (1961; Zbl 0123.032)].