INSERTION-OF-FACTORS-PROPERTY ON SKEW POLYNOMIAL RINGS

In this paper, we investigate the insertion-of-factors-property (simply, IFP) on skew polynomial rings, introducing the concept of strongly sigma-IFP for a ring endomorphism sigma. A ring R is said to have 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.