Geodesic
Lattice of all topologies of countable module over countable rings
Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica, no. 2 (2016), pp. 63-70 
V. I. Arnautov; G. N. Ermakova. Lattice of all topologies of countable module over countable rings. Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica, no. 2 (2016), pp. 63-70. http://geodesic.mathdoc.fr/item/BASM_2016_2_a5/
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Voir la notice de l'article provenant de la source Math-Net.Ru

For any countable ring $R$ with discrete topology $\tau_0$ and any countable $R$-module $M$ the lattice of all $(R,\tau_0)$-module topologies contains: – A sublattice which is isomorphic to the lattice of all real numbers with the usual order; – Two to the power of continuum $(R,\tau_0)$-module topologies each of which is a coatom.

[1] Arnautov V. I., Glavatsky S. T., Mikhalev A. V., Introduction to the theory of topological rings and modules, Marcel Dekker, inc., New York–Basel–Hong Kong, 1996, 502 pp. | MR | Zbl

[2] Arnautov V. I., “On topologization of infinite modules”, Mat. Issled., 7:4 (1972), 241–243 (in Russian) | MR | Zbl

[3] Arnautov V. I., Ermakova G. N., “On the number of metrizable group topologies on countable groups”, Bul. Acad. Ştiinţe Repub. Moldova, Mat., 2013, no. 2(72)–3(73), 17–26 | MR | Zbl

[4] Arnautov V. I., Ermakova G. N., “On the number of group topologies on countable groups”, Bul. Acad. Ştiinţe Repub. Moldova, Mat., 2014, no. 1(74), 101–112 | MR | Zbl

[5] Arnautov V. I., Ermakova G. N., “On the number of ring topologies on countable rings”, Bul. Acad. Ştiinţe Repub. Moldova, Mat., 2015, no. 1(77), 103–114 | MR