Authors: Arnautov Vladimir, G. N. Ermakova
Abstract
For any countable ring $ R $ and any non-discrete metrizable
ring topology $ \tau _0 $, the lattice of all ring topologies
admits:
\newline
-- Continuum of non-discrete metrizable ring topologies stronger
than the given topo\-logy $ \tau _0 $ and such that $ \sup \{\tau
_1, \tau _2 \} $ is the discrete topology for any different
topologies;
\newline
-- Continuum of non-discrete metrizable ring topologies stronger
than $ \tau _0 $ and such that any two of these topologies are
comparable;
\newline
-- Two to the power of continuum of ring topologies stronger
than $ \tau _0 $, each of them being a coatom in the lattice of
all ring topologies.
V. I. Arnautov
Institute of Mathematics and Computer Science
Academy of Sciences of Moldova
5 Academiei str., MD-2028, Chisinau
Moldova
E-mail: G. N. Ermacova
Transnistrian State University
25 October str., 128, Tiraspol, 278000
Moldova
E-mail:
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