%0 Journal Article
%T Extensions of strongly \alpha-reversible rings
%J Bulletin of the Iranian Mathematical Society
%I Iranian Mathematical Society (IMS)
%Z 1017-060X
%A Zhao, L.
%A Zhu, X.
%D 2012
%\ 04/01/2012
%V 38
%N 1
%P 275-292
%! Extensions of strongly \alpha-reversible rings
%K reversible rings
%K strongly $\alpha$-reversible rings
%K Nil-$\alpha$-reversible rings
%K weakly reversible rings
%R
%X We introduce the notion ofstrongly $\alpha$-reversible rings which is a strong version of$\alpha$-reversible rings, and investigate its properties. We firstgive an example to show that strongly reversible rings need not bestrongly $\alpha$-reversible. We next argue about the strong$\alpha$-reversibility of some kinds of extensions. A number ofproperties of this version are established. It is shown that a ring$R$ is strongly right $\alpha$-reversible if and only if itspolynomial ring $R[x]$ is strongly right $\alpha$-reversible if andonly if its Laurent polynomial ring $R[x, x^{-1}]$ is strongly right$\alpha$-reversible. Moreover, we introduce the concept ofNil-$\alpha$-reversible rings to investigate the nilpotent elementsin $\alpha$-reversible rings. Examples are given to show that rightNil-$\alpha$-reversible rings need not be right $\alpha$-reversible.
%U http://bims.iranjournals.ir/article_406_9c2daebbe954621c0aa88d44f49c476e.pdf