@article { author = {Azimi, M. and Moussavi, A.}, title = {Nilpotent Elements in Skew Polynomial Rings}, journal = {Journal of Sciences, Islamic Republic of Iran}, volume = {28}, number = {1}, pages = {59-74}, year = {2017}, publisher = {University of Tehran}, issn = {1016-1104}, eissn = {2345-6914}, doi = {}, abstract = { 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.}, keywords = {compatible ring,skew polynomial ring,skew power series ring}, url = {https://jsciences.ut.ac.ir/article_59401.html}, eprint = {https://jsciences.ut.ac.ir/article_59401_44b5ba26e8aa2361d06eeccfe325849c.pdf} }