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## Properties of finite unrefinable chains of ring topologies for nilpotent rings

Authors: Arnautov Vladimir, G. N. Ermakova

### Abstract

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 $\tau_0\prec_ {\mathfrak {M}} \tau_1\prec _ {\mathfrak {M}} \ldots\prec_{\mathfrak {M}} \tau_n$ is an unrefinable chain of ring topologies from $\mathfrak {M}$ and $\tau\in\mathfrak {M}$, then $k\leq n$ for any chain $\sup\{\tau,\tau ' _0\} =\tau ' _1 <\tau ' _2 <\ldots <\tau ' _k =\sup\{\tau,\tau _n\}$ of topologies from $\mathfrak {M}$.

V. I.Arnautov
Institute of Mathematics and Computer Science
Chisinau, Moldova
E-mail:

G. N.Ermacova
Transnistrian State University
25 October str., 128, Tiraspol, 278000
Moldova
E-mail:

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