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IMCS/Publications/BASM/Issues/BASM n.1(86), 2018/

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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