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 
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/
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Voir la notice de l'article provenant de la source Math-Net.Ru

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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