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## Unrefinable chains when taking the infimum in the lattice of ring topologies for a nilpotent ring

Authors: G. N. Ermakova

### Abstract

A nilpotent ring $\widehat{R}$ and two ring topologies $\widehat{\tau}''$ and $\widehat{\tau}*$ on $\widehat{R}$ are constructed such that $\widehat{\tau}*$ is a coatom (i.e. between the discrete topology $\tau_d$ and $\widehat\tau*$ there no exists ring topologies) and such that between $\inf \{\widehat{\tau}'',\widehat{\tau}_d \}$ and $\inf \{\widehat{\tau}'',\widehat\tau* \}$ there exists an infinite chain of ring topologies in the lattice of all ring topologies of the ring $\widehat{R}$.

V. I. Arnautov
Institute of Mathematics and Computer Science