RO  EN

## 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