Rings with finite decomposition of identity

A criterion for semiprime rings with finite decomposition of identity to be prime is given. We also give a short survey on some finiteness conditions related to the decomposition of identity. We consider the notion of a net of a ring and show that the lattice of all two-sided ideals of a right semidistributive semiperfect ring is distributive. An application of decompositions of identity to groups of units is given.Наведено критерiй первинностi напiвпервинних кiлець iз скiнченним розкладом одиницi, а також короткий огляд деяких умов скiнченностi вiдносно розкладу одиницi. Розглянуто поняття сiтки кiльця i показано, що решiтка всiх двобiчних iдеалiв правого напiвдистрибутивного напiвдосконалого кiльця є дистрибутивною. Наведено застосування розкладу одиницi до груп одиниць

On some developments in investigation of groups with prescribed properties of generalized normal subgroups

The survey is dedicated to investigation of groups with prescribed properties of generalized normal subgroups. The roots of such investigations lie in the works by R. Dedekind, R. Baer, O.Yu.Schmidt, and S.N. Chernikov. The main goal of this survey is to reflect some important developments in this area

On some aspects of the theory of modules over group rings

The authors discuss some recent developments in the theory of modules over group rings

5th International Algebraic Conference in Ukraine

This volume contains papers based on the talks presented at the 5t h In- ternational Algebraic Conference in Ukraine, which took place in Ode ssa on July 20–27, 2005. The conference was organized by Odessa I. I. M ech- nikov National University, Kyiv Taras Shevchenko National Univers ity, Institute of Mathematics of National Academy of Sciences of Ukrain e, Odessa A. S. Popov National Academy of Communication and Lugansk Taras Shevchenko National Pedagogical University

Quivers of 3×3 exponent matrices

We show how to use generating exponent matrices to study the quivers of exponent matrices. We also describe the admissible quivers of 3×3 exponent matrices

Quivers of 3×3-exponent matrices

We show how to use generating exponent matrices to study the quivers of exponent matrices. We also describe the admissible quivers of 3×3 exponent matrices

Techniques and technologies of definition of the contents of uranium and plutonium isotopes in radioactive waste

In this review, the issues of radiation and nucleus safety at dealing with nuclear waste (RW) are considered. The examples of already worked out technologies on definition of the isotopes contents of uranium and plutonium in radioactive waste are adduced; the possibilities of implementation of techniques with application of electron linac are shown.Розглянуто питання забезпечення радіаційної та ядерної безпеки при роботі з радіоактивними відходами (РАВ). Наведено приклади вже розроблених технологій з визначення вмісту ізотопів урану і плутонію в радіоактивних відходах, показано можливості реалізації методик з використанням лінійних прискорювачів електронів.Рссмотрены вопросы обеспечения радиационной и ядерной безопасности при обращении с радиоактивными отходами (РАО). Приведены примеры уже разработанных технологий по определению содержания изотопов урана и плутония в радиоактивных отходах, показаны возможности реализации методик с применением линейных ускорителей электронов

Some related to pronormality subgroup families and the properties of a group

Some influential families of subgroups such as pronormal subgroups, contranormal subgroups, and abnormal subgroups, their generalizations, characterizations, interplays between them and the group, and their connections to other types of subgroups have been considered

Determination of the ²³⁸U concentration in concrete samples by registration of fission neutrons

In the work was to carry out and to improve the fission elements content tests of techniques for the concrete samples analysis of weight up to 0.5 kgs. The basis of this technique is the active analysis. Researched samples were irradiated with flows of neutrons received on the basis of the electron linear accelerator. The neutrons induce fissions in the samples. Experiment was carried out at ELE - 300 NSC KIPT. The technique allowing expressly, with a sufficient degree of reliability is checked up in operation to define the contents ²³⁸U in concrete samples. Achieved in the given experiment sensitivity makes ~ 10 g of uranium in a sample

On Baer-Shemetkov’s decomposition in modules and related topics

This article is dedicated to the memory of an outstanding algebraist Leonid A. Shemetkov. His ideas and results not only shaped modern soluble finite group theory, but significantly influenced other branches of algebra. In this article, we traced the influence of L.A. Shemetkov's ideas on some areas of modules theory and infinite groups theory