RO EN
Properties of finite unrefinable chains of ring topologies for nilpotent rings
Authors: Arnautov Vladimir, G. N. Ermakova
– 0.13 Mb
Abstract
Let $R $ be a nilpotent ring and let $ (\mathfrak {M}, <) $ be the lattice of all ring topologies or the lattice of all ring topologies in each of which the ring $R $ possesses a basis of neighborhoods of zero consisting of subgroups. If $ \tau_0\prec_ {\mathfrak {M}} \tau_1\prec _ {\mathfrak {M}} \ldots\prec_{\mathfrak {M}} \tau_n $ is an unrefinable chain of ring topologies from $ \mathfrak {M} $ and $\tau\in\mathfrak {M}$, then $k\leq n $ for any chain $\sup\{\tau,\tau ' _0\} =\tau ' _1 <\tau ' _2 <\ldots <\tau ' _k =\sup\{\tau,\tau _n\} $ of topologies from $ \mathfrak {M} $.V. I.Arnautov
Institute of Mathematics and Computer Science
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
Chisinau, Moldova
E-mail:
G. N.Ermacova
Transnistrian State University
25 October str., 128, Tiraspol, 278000
Moldova
E-mail:
Fulltext
– 0.13 Mb
Contents
- Shape dimension of maps
- Semi-integral filters and semi-integral BL-algebras
- Orthogonality and retract orthogonality of operations
- An Approach for Determining the Optimal Strategies for an Average Markov Decision Problem with Finite State and Action Spaces
- The Center of the Lattice of Factorization Structures
- Properties of finite unrefinable chains of ring topologies for nilpotent rings
- Quartic differential systems with an invariant straight line of maximal multiplicity
- Distances on Free Semigroups and Their Applications
- Integrability conditions for a class of cubic differential systems with a bundle of two invariant straight lines and one invariant cubic
