Properties of finite unrefinable chains of ring topologies for nilpotent rings

V. I. Arnautov ; G. N. Ermakova

Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica, no. 1 (2018), pp. 67-75.

Résumé

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 ${\tau }_0{\prec }_{\mathfrak{M}}{\tau }_1{\prec }_{\mathfrak{M}}\cdots {\prec }_{\mathfrak{M}}{\tau }_n$ is an unrefinable chain of ring topologies from $\mathfrak{M}$ and $\tau \in \mathfrak{M}$, then $k\le n$ for any chain $sup\{\tau ,{\tau }_0^{\prime }\}={\tau }_1^{\prime }{\tau }_2^{\prime }\dots {\tau }_k^{\prime }=sup\{\tau ,{\tau }_n\}$ of topologies from $\mathfrak{M}$.

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