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## Lattice of all topologies of countable module over countable rings

Authors: Arnautov Vladimir, G. N. Ermakova

### Abstract

For any countable ring $R$ with discrete topology $\tau _0$ and any countable $R$-module $M$ the lattice of all $(R, \tau _0)$-module topologies contains: \newline -- A sublattice which is isomorphic to the lattice of all real numbers with the usual order; \newline -- Two to the power of continuum $(R, \tau _0)$-module topologies each of which is a coatom.

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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