On the number of ring topologies on countable rings

V. I. Arnautov ; G. N. Ermakova

Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica, no. 1 (2015), pp. 103-114.

Résumé

For any countable ring $R$ and any non-discrete metrizable ring topology ${\tau }_0$, the lattice of all ring topologies admits: – Continuum of non-discrete metrizable ring topologies stronger than the given topology ${\tau }_0$ and such that $sup\{{\tau }_1,{\tau }_2\}$ is the discrete topology for any different topologies; – Continuum of non-discrete metrizable ring topologies stronger than ${\tau }_0$ and such that any two of these topologies are comparable; – 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.

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