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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