On equivalence of some subcategories of modules in Morita contexts
Algebra and discrete mathematics, no. 3 (2003), pp. 46-53.

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A Morita context $(R,\,_RV_S,\,_SW_R,\,S)$ defines the isomorphism $\mathcal L_0(R)\cong\mathcal L_0(S)$ of lattices of torsions $r\geq r_I$ of $R$-$Mod$ and torsions $s\geq r_J$ of $S$-$Mod$, where $I$ and $J$ are the trace ideals of the given context. For every pair $(r,s)$ of corresponding torsions the modifications of functors $T^W=W\otimes_{R^-}$ and $T^V=V\otimes_{S^-}$ are considered: \begin{equation*} R\textrm{-}Mod\supseteq\mathcal P(r) ???????????? \mathcal P(s)\subseteq S\textrm{-}Mod, \end{equation*} where $\mathcal P(r)$ and $\mathcal P(s)$ are the classes of torsion free modules. It is proved that these functors define the equivalence \begin{equation*} \mathcal P(r)\cap\mathcal J_I\approx\mathcal P(s)\cap\mathcal J_J, \end{equation*} where $\mathcal P(r)=\{_RM\mid r(M)=0\}$ and $\mathcal J_I=\{_RM\mid IM=M\}$.
Keywords: torsion (torsion theory)
Mots-clés : Morita context, torsion free module, accessible module, equivalence.
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     author = {A. I. Kashu},
     title = {On equivalence of some subcategories of modules in {Morita} contexts},
     journal = {Algebra and discrete mathematics},
     pages = {46--53},
     publisher = {mathdoc},
     number = {3},
     year = {2003},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ADM_2003_3_a2/}
}
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A. I. Kashu. On equivalence of some subcategories of modules in Morita contexts. Algebra and discrete mathematics, no. 3 (2003), pp. 46-53. http://geodesic.mathdoc.fr/item/ADM_2003_3_a2/