INSERTION-OF-FACTORS-PROPERTY ON SKEW POLYNOMIAL RINGS
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In this paper, we investigate the insertion-of-factors-proper- ty (simply, IFP) on skew polynomial rings, introducing the concept of strongly σ-IFP for a ring endomorphism σ. A ring R is said to have strongly σ-IFP if the skew polynomial ring R[x; σ] has IFP. We examine some characterizations and extensions of strongly σ-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.
Abstract
In this paper, we investigate the insertion-of-factors-proper- ty (simply, IFP) on skew polynomial rings, introducing the concept of strongly σ-IFP for a ring endomorphism σ. A ring R is said to have strongly σ-IFP if the skew polynomial ring R[x; σ] has IFP. We examine some characterizations and extensions of strongly σ-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.
참고문헌 (26)
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