Geodesic
On localizations in Morita contexts
Sbornik. Mathematics, Tome 61 (1988) no. 1, pp. 129-135 
A. I. Kashu. On localizations in Morita contexts. Sbornik. Mathematics, Tome 61 (1988) no. 1, pp. 129-135. http://geodesic.mathdoc.fr/item/SM_1988_61_1_a8/
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     title = {On localizations in {Morita} contexts},
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     url = {http://geodesic.mathdoc.fr/item/SM_1988_61_1_a8/}
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Voir la notice de l'article provenant de la source Math-Net.Ru

A Morita context $(R,{}_RU_S,{}_SV_R,S)$ with a mapping $(\;{,}\;)\colon U\otimes_SV\to R$ defines for every $M\in{}_R\mathscr M$ a canonical homomorphism $\varphi_M\colon M\to \operatorname{Hom}_S(V,\operatorname{Hom}_R(U,M))$. Necessary and sufficient conditions are found for $\varphi_M$ to be an $r_I$-localization of the module $M$ for every $M\in{}_R\mathscr M$, where $r_I$ is the ideal torsion defined by the ideal $I=(U,V)$ of the ring $R$. In particular, these conditions are satisfied when ${}_R(U\otimes _SV)$ is a projective module with trace $I$. Bibliography: 9 titles.

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[6] Kato T., “Duality between colocalization and localization”, J. Algebra, 55:2 (1978), 351–374 | DOI | MR | Zbl

[7] Cohn P. M., “Morita equivalence and duality”, Queen Mary College Math. Notes, London, 1966

[8] Müller B. J., “The quotient category of a Morita context”, J. Algebra, 28:3 (1974), 389–407 | DOI | MR | Zbl

[9] Feis K., Algebra: koltsa, moduli, kategorii, t. 1, Mir, M., 1977