Geodesic
Properties of finite unrefinable chains of ring topologies for nilpotent rings
Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica, no. 1 (2018), pp. 67-75.

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Let $R$ be a nilpotent ring and let $(\mathfrak M,)$ be the lattice of all ring topologies or the lattice of all ring topologies in each of which the ring $R$ possesses a basis of neighborhoods of zero consisting of subgroups. If $\tau_0\prec_\mathfrak M\tau_1\prec_\mathfrak M\dots\prec_\mathfrak M\tau_n$ is an unrefinable chain of ring topologies from $\mathfrak M$ and $\tau\in\mathfrak M$, then $k\leq n$ for any chain $\sup\{\tau,\tau'_0\}=\tau'_1\tau'_2\dots\tau'_k=\sup\{\tau,\tau_n\}$ of topologies from $\mathfrak M$. 
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V. I. Arnautov; G. N. Ermakova. Properties of finite unrefinable chains of ring topologies for nilpotent rings. Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica, no. 1 (2018), pp. 67-75. http://geodesic.mathdoc.fr/item/BASM_2018_1_a5/

[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 | MR | Zbl

[2] Arnautov V. I., Topala A. Gh., “An example of ring with non-modular lattice of ring topologies”, Buletinul A.Ş.R.M. Matematica, 1998, no. 2(27), 130–131 | MR | Zbl

[3] Birkhoff G., Lattice theory, Nauka, Moscow, 1984 (in Russian) | MR

[4] Arnautov V. I., “Properties of final unrefinable chains of groups topologies”, Bul. Acad. Repub. Moldova. Matematica, 2010, no. 2(63), 3–19 | MR | Zbl

[5] Grätzer G., General lattice theory, Mir, Moscow, 1982 (in Russian) | MR | Zbl

[6] Kurosh A. G., Lectures on general algebra, Moscow, 2007 (in Russian) | MR

[7] Smarda B., “The lattice of topologies of topological $l$-group”, Czechosl. Math. Jour., 26:101 (1976), 128–136 | MR | Zbl

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

[9] Arnautov V. I., Ermakova G. N., “Unrefinable chains when taking the infimum in the lattice of ring topologies for a nilpotent ring”, Bul. Acad. Repub. Moldova. Matematica, 2017, no. 2(84), 71–76 | MR | Zbl