Institutul de Matematică şi Informatică "Vladimir Andrunachievici"
Universitatea de Stat din MoldovaRO EN
Properties of coverings in lattices of ring topologies
Authors: Arnautov Vladimir, G., N., Ermakova
Keywords: Ring, ideal, lattice of ring topologies, unrefinable chain of ring topologies, supremum of ring topologies, basis of filter of neighborhoods of zero, semidirect product of rings, restriction of ring topologies to an ideal, cover of an element in a lattice
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Keywords: Ring, ideal, lattice of ring topologies, unrefinable chain of ring topologies, supremum of ring topologies, basis of filter of neighborhoods of zero, semidirect product of rings, restriction of ring topologies to an ideal, cover of an element in a lattice
Abstract
When studying unrefinable chains of ring topologies, it is natural to find out how neighborhoods of zero of ring topologies in such chains are related to each other. \newline It is proved that for any ideal the restrictions of these topologies to the ideal coincides, or the sum of any neighborhood of zero in the stronger topology with the intersection of the ideal with any neighborhood of zero in the weaker topology is a neighborhood of zero in the weaker topology. We construct a ring and two ring topologies which form an unrefinable chain in the lattice of all ring topologies that a basis of filter of neighborhoods of zero which consists of subgroups of the additive group of the ring and restriction of these topologies to some ideal of the ring is no longer a unrefinable chain. This example shows that the given in [4] conditions under which the properties of a unrefinable chain of ring topologies, are preserved under taking the supremum are essential.V. I. Arnautov
Vladimir Andrunachievici Institute of Mathematics
and Computer Science
5 Academiei str., MD-2028, Chisinau
Moldova
E-mail:
G. N. Ermakova
Transnistrian State University
25 October str., 128, Tiraspol, 278000
Moldova
E-mail:
Vladimir Andrunachievici Institute of Mathematics
and Computer Science
5 Academiei str., MD-2028, Chisinau
Moldova
E-mail:
G. N. Ermakova
Transnistrian State University
25 October str., 128, Tiraspol, 278000
Moldova
E-mail:
DOI
https://doi.org/10.56415/basm.y2022.i1.p66Fulltext
– 0.13 Mb
Contents
- Continuous Extensions On Euclidean Combinatorial Configurations
- Subordination and superordination for certain analytic functions associated with Ruscheweyh derivative and a new generalised multiplier transformation
- Different Types of Compact Global Attractors for Cocycles with a Noncompact Phase Space of Driving System and the Relationship Between Them
- A New Method for Developing Signature Algorithms on Finite Non-commutative Algebras
- Properties of coverings in lattices of ring topologies
- Equilibria in Pure Strategies for a Two-Player Zero-Sum Average Stochastic Positional Game
- Morita Contexts, Preradicals and Closure Operators in Modules
- A self--similar solution and the tanh--function method for the kinetic Carleman system
