Geodesic
Bezout rings, annihilators, and diagonalizability
Fundamentalʹnaâ i prikladnaâ matematika, Tome 21 (2016) no. 2, pp. 253-256.

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Let $A$ be a right invariant ring. If $A$ is a diagonalizable ring or an exchange Bezout ring, then $B + r(M) = r(M/MB)$ for every finitely generated right $A$-module $M$ and any ideal $B$ of the ring $A$. 
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A. A. Tuganbaev. Bezout rings, annihilators, and diagonalizability. Fundamentalʹnaâ i prikladnaâ matematika, Tome 21 (2016) no. 2, pp. 253-256. http://geodesic.mathdoc.fr/item/FPM_2016_21_2_a11/

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