Institutul de Matematică şi Informatică "Vladimir Andrunachievici"
Universitatea de Stat din MoldovaRO EN
Unrefinable chains when taking the infimum in the lattice of ring topologies for a nilpotent ring
Authors: G. N. Ermakova
– 0.10 Mb
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:
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:
Fulltext
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Contents
- Vladimir A. Andrunachievici (1917 - 1997)
- Early History of the Theory of Rings in Novosibirsk
- Pretorsions in modules and associated closure operators
- Properties of accessible subrings of pseudonormed rings when taking quotient rings
- Radicals and generalizations of derivations
- Some examples of topological modules
- Unrefinable chains when taking the infimum in the lattice of ring topologies for a nilpotent ring
- On the inverse operations in the class of preradicals of a module category, II
- On LCA groups whose ring of continuous endomorphisms satisfies DCC on closed ideals
- The Lyapunov quantities and the center conditions for a class of bidimensional polynomial systems of differential equations with nonlinearities of the fourth degree
