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Department of of Mathematical Sciences, Isfahan University of Technology, Isfahan 84156-83111,
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.
Tolooei, Y., & Vedadi, M. R. (2014). Reversibility of a module with respect to the bifunctors Hom and Rej. Bulletin of the Iranian Mathematical Society, 40(4), 931-940.
MLA
Y. Tolooei; M. R. Vedadi. "Reversibility of a module with respect to the bifunctors Hom and Rej". Bulletin of the Iranian Mathematical Society, 40, 4, 2014, 931-940.
HARVARD
Tolooei, Y., Vedadi, M. R. (2014). 'Reversibility of a module with respect to the bifunctors Hom and Rej', Bulletin of the Iranian Mathematical Society, 40(4), pp. 931-940.
VANCOUVER
Tolooei, Y., Vedadi, M. R. Reversibility of a module with respect to the bifunctors Hom and Rej. Bulletin of the Iranian Mathematical Society, 2014; 40(4): 931-940.
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