Iranian Mathematical Society (IMS)Bulletin of the Iranian Mathematical Society1017-060X38120120401Extensions of strongly \alpha-reversible rings275292406ENL.ZhaoNanjing UniversityX.ZhuNanjing UniversityJournal Article20090923We introduce the notion of<br />strongly $\alpha$-reversible rings which is a strong version of<br />$\alpha$-reversible rings, and investigate its properties. We first<br />give an example to show that strongly reversible rings need not be<br />strongly $\alpha$-reversible. We next argue about the strong<br />$\alpha$-reversibility of some kinds of extensions. A number of<br />properties of this version are established. It is shown that a ring<br />$R$ is strongly right $\alpha$-reversible if and only if its<br />polynomial ring $R[x]$ is strongly right $\alpha$-reversible if and<br />only if its Laurent polynomial ring $R[x, x^{-1}]$ is strongly right<br />$\alpha$-reversible. Moreover, we introduce the concept of<br />Nil-$\alpha$-reversible rings to investigate the nilpotent elements<br />in $\alpha$-reversible rings. Examples are given to show that right<br />Nil-$\alpha$-reversible rings need not be right $\alpha$-reversible.http://bims.iranjournals.ir/article_406_9c2daebbe954621c0aa88d44f49c476e.pdf