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IMI/Publicaţii/BASM/Ediţii/BASM n.1 (77), 2015/

On the number of ring topologies on countable rings

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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