Geodesic
Unrefinable chains when taking the infimum in the lattice of ring topologies for a nilpotent ring
Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica, no. 2 (2017), pp. 71-76 
V. I. Arnautov; G. N. Ermakova. Unrefinable chains when taking the infimum in the lattice of ring topologies for a nilpotent ring. Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica, no. 2 (2017), pp. 71-76. http://geodesic.mathdoc.fr/item/BASM_2017_2_a5/
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     title = {Unrefinable chains when taking the infimum in the lattice of ring topologies for a~nilpotent ring},
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Voir la notice de l'article provenant de la source Math-Net.Ru

A nilpotent ring $\widehat R$ and two ring topologies $\widehat\tau''$ and $ \widehat\tau*$ on $\widehat R$ are constructed such that $\widehat\tau*$ is a coatom (i.e. between the discrete topology $\tau_d$ and $\widehat\tau*$ there no exists ring topologies) and such that between $\inf\{\widehat\tau'',\widehat\tau_d\}$ and $\inf\{\widehat\tau'',\widehat\tau*\}$ there exists an infinite chain of ring topologies in the lattice of all ring topologies of the ring $\widehat R$.

[1] Arnautov V. I., Topala A. Gh., “An example of ring with non-modular lattice of ring topologies”, Bul. Acad. Ştiinţe Repub. Moldova, Mat., 1998, no. 2(27), 130–131 | MR | Zbl

[2] Arnautov V. I., “Svoystva konechnyh neuplotniaemyh tzepochek kolitzevyh topologiy”, Fundamentalinaia i prikladnaia matematika, 16:8 (2010), 5–16 (in Russian) | MR

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