Application of the lattice methods for investigation of topologies in groups and rings, of torsions in modules and of hyperbolic varieties

Programmee:Institutional Projects (Supreme Council for Science and Technological Development)
Execution period:2006 – 2010
Institutions:Academy of Sciences of Moldova, Institute of Mathematics and Computer Science
Project Leader:Kashu Alexei
Participants: Kashu Alexei, Arnautov Vladimir, Popa Valeriu, Gutsul Ion, Damian Florin, Zamorzaeva Elizaveta
Field of application:Fundamental Sciences - Physics-Mathematics
Keywords:geometry of hyperbolic varieties


A sufficiently general method for construction of a group topology which precedes a given linear and metrizable topology will be developed for abelian groups of finite order. The groups of different classes of local compact abelian groups, with the property that their ring of continuous endomorphisms is commutative, will be described. The main classes of modules, related with radicals and torsions in the category of modules will be studied, the properties of the lattices determined by these classes will be shown, as well as the description of them in terms of the ring. The investigations related to geometry of complete and incomplete 2-5 dimensions hyperbolic varieties, as well as to the corresponding decompositions of their universal coverages will be carried out.