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Nilpotent Elements in Skew Polynomial Rings | ||
| Journal of Sciences, Islamic Republic of Iran | ||
| مقاله 5، دوره 28، شماره 1، فروردین 2017، صفحه 59-74 اصل مقاله (474.67 K) | ||
| نوع مقاله: Final File | ||
| نویسندگان | ||
| M. Azimi؛ A. Moussavi* | ||
| Department of Pure Mathematics, Faculty of Mathematical Sciences, Tarbiat Modares University, P.O. Box 14115-134, Tehran, Islamic Republic of Iran | ||
| چکیده | ||
| Letbe a ring with an endomorphism and an -derivationAntoine studied the structure of the set of nilpotent elements in Armendariz rings and introduced nil-Armendariz rings. In this paper we introduce and investigate the notion of nil--compatible rings. The class of nil--compatible rings are extended through various ring extensions and many classes of nil--compatible rings are constructed. We also prove that, if is nil--compatible and nil-Armendariz ring of power series type with nilpotent, then . We show that, if is a nil-Armendariz ring of power series type, with nilpotent and nil--compatible ring, then As a consequence, several known results are unified and extended to the more general setting. Also examples are provided to illustrate our results. | ||
| کلیدواژهها | ||
| compatible ring؛ skew polynomial ring؛ skew power series ring | ||
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