@article { author = {Tolooei, Y. and Vedadi, M. R.}, title = {Reversibility of a module with respect to the bifunctors Hom and‎ ‎Rej}, journal = {Bulletin of the Iranian Mathematical Society}, volume = {40}, number = {4}, pages = {931-940}, year = {2014}, publisher = {Iranian Mathematical Society (IMS)}, issn = {1017-060X}, eissn = {1735-8515}, doi = {}, abstract = {Let $M_R$ be a non-zero‎ ‎module and ${\mathcal F}‎: ‎\sigma[M_R]\times \sigma[M_R]‎ ‎\rightarrow$ Mod-$\Bbb{Z}$ a bifunctor‎. ‎The‎ ‎$\mathcal{F}$-reversibility of $M$ is defined by ${\mathcal‎ ‎F}(X,Y)=0 \Rightarrow {\mathcal F}(Y,X)=0$ for all non-zero $X,Y$‎ ‎in $\sigma[M_R]$‎. ‎Hom (resp‎. ‎Rej)-reversibility of $M$ is‎ ‎characterized in different ways‎. ‎Among other things‎, ‎it is shown‎ ‎that $R_R$ {\rm($_RR$)} is Hom-reversible if and only if $R =‎ ‎\bigoplus_{i=1}^n R_i$ such that each $R_i$ is a perfect ring with‎ ‎a unique simple module (up to isomorphism)‎. ‎In particular‎, ‎for a‎ ‎duo ring‎, ‎the concepts of perfectness and Hom-reversibility‎ ‎coincide‎.}, keywords = {Co-retractable‎,‎Kasch module‎,‎perfect ring‎,‎prime module‎,‎cogenerator‎}, url = {http://bims.iranjournals.ir/article_542.html}, eprint = {http://bims.iranjournals.ir/article_542_aa4318fb32317b7ebcdad5b47acfa0d1.pdf} }