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IMI/Publicaţii/BASM/Ediţii/BASM n.2(84), 2017/

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
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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