RO EN
On the number of ring topologies on countable rings
Authors: Arnautov Vladimir, G. N. Ermakova
– 0.14 Mb
Abstract
For any countable ring $ R $ and any non-discrete metrizable ring topology $ \tau _0 $, the lattice of all ring topologies admits: \newline -- Continuum of non-discrete metrizable ring topologies stronger than the given topo\-logy $ \tau _0 $ and such that $ \sup \{\tau _1, \tau _2 \} $ is the discrete topology for any different topologies; \newline -- Continuum of non-discrete metrizable ring topologies stronger than $ \tau _0 $ and such that any two of these topologies are comparable; \newline -- 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.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
– 0.14 Mb
Contents
- On fixed point subalgebras of some local algebras over a field
- Stability radius bounds in multicriteria Markowitz portfolio problem with venturesome investor criteria
- lp(R)-equivalence of topological spaces and topological modules
- One subfamily of cubic systems with invariant lines of total multiplicity eight and with two distinct real infinite singularities
- Primary decomposition of general graded structures
- On the distinction between one-dimensional Euclidean and hyperbolic spaces
- On the number of ring topologies on countable rings
- Determining the Optimal Evolution Time for Markov Processes with Final Sequence of States
