Extensions of strongly alpha-reversible rings
(ندگان)پدیدآور
Zhao, L.Zhu, X.نوع مدرک
TextResearch Paper
زبان مدرک
Englishچکیده
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.
کلید واژگان
reversible ringsstrongly $alpha$-reversible rings
Nil-$alpha$-reversible rings
weakly reversible rings
شماره نشریه
1تاریخ نشر
2012-04-011391-01-13
ناشر
Springer and the Iranian Mathematical Society (IMS)سازمان پدید آورنده
Nanjing UniversityNanjing University
شاپا
1017-060X1735-8515