TY - JOUR
ID - 406
TI - Extensions of strongly \alpha-reversible rings
JO - Bulletin of the Iranian Mathematical Society
JA - BIMS
LA - en
SN - 1017-060X
AU - Zhao, L.
AU - Zhu, X.
AD - Nanjing University
Y1 - 2012
PY - 2012
VL - 38
IS - 1
SP - 275
EP - 292
KW - reversible rings
KW - strongly $\alpha$-reversible rings
KW - Nil-$\alpha$-reversible rings
KW - weakly reversible rings
DO -
N2 - 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.
UR - http://bims.iranjournals.ir/article_406.html
L1 - http://bims.iranjournals.ir/article_406_9c2daebbe954621c0aa88d44f49c476e.pdf
ER -