Journal of the
Korean Mathematical Society JKMS

In this paper, we investigate the insertion-of-factors-proper\-ty (simply, IFP) on skew polynomial rings, introducing the concept of strong\-ly $\sigma$-IFP for a ring endomorphism $\sigma$. A ring $R$ is said to have \emph{strongly $\sigma$-IFP} if the skew polynomial ring $R[x;\sigma]$ has IFP. We examine some characterizations and extensions of strongly $\sigma$-IFP rings in relation with several ring theoretic properties which have important roles in ring theory. We also extend many of related basic results to the wider classes, and so several known results follow as consequences of our results.

Keywords: strongly $\sigma$-IFP ring, (strongly) IFP ring, $\sigma$-rigid ring, skew polynomial ring, Dorroh extension, matrix ring

MSC numbers: Primary 16W20, 16U80; Secondary 16S36