Geodesic
Annihilators and finitely generated modules
Fundamentalʹnaâ i prikladnaâ matematika, Tome 21 (2016) no. 1, pp. 79-82 
E. S. Golod; A. A. Tuganbaev. Annihilators and finitely generated modules. Fundamentalʹnaâ i prikladnaâ matematika, Tome 21 (2016) no. 1, pp. 79-82. http://geodesic.mathdoc.fr/item/FPM_2016_21_1_a6/
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Voir la notice de l'article provenant de la source Math-Net.Ru

We prove that $B + \mathrm{Ann}\, M = \mathrm{Ann}\, (M/MB)$ for every finitely generated right module $M$ over a strongly regular ring $A$ and every ideal $B$ of the ring $A$.

[1] Golod E. S., “Zamechanie o kommutativnykh arifmeticheskikh koltsakh”, Fundament. i prikl. matem., 19:2 (2014), 21–23

[2] Goodearl K. R., Von Neumann Regular Rings, Pitman, London, 1979 | MR | Zbl

[3] Wisbauer R., Foundations of Module and Ring Theory, Gordon and Breach, Philadelphia, 1991 | MR | Zbl