Algebra and Discrete Mathematics, 2007, № 3 http://dspace.nbuv.gov.ua:80/handle/123456789/150348 2026-04-22T14:32:33Z 2026-04-22T14:32:33Z There isn’t much duality in radical theory Gardner, B.J. http://dspace.nbuv.gov.ua:80/handle/123456789/152372 2019-06-10T22:25:22Z 2007-01-01T00:00:00Z There isn’t much duality in radical theory Gardner, B.J. The definitions of radical and semi-simple classes are in a natural sense dual to each other. However, statements dual in the same sense to theorems of radical theory tend to be false. Some insights may nevertheless be gained from consideration of duality, and we illustrate this with a link between additive radicals and semi-simple radical classes. 2007-01-01T00:00:00Z Groups whose non-normal subgroups have small commutator subgroup De Falco, M. de Giovanni, F. Musella, C. http://dspace.nbuv.gov.ua:80/handle/123456789/152371 2019-06-10T22:25:23Z 2007-01-01T00:00:00Z Groups whose non-normal subgroups have small commutator subgroup De Falco, M.; de Giovanni, F.; Musella, C. The structure of groups whose non-normal subgroups have a finite commutator subgroup is investigated. In particular, it is proved that if k is a positive integer and G is a locally graded group in which every non-normal subgroup has finite commutator subgroup of order at most k, then the commutator subgroup of G is finite. Moreover, groups with finitely many normalizers of subgroups with large commutator subgroup are studied. 2007-01-01T00:00:00Z On sum of a nilpotent and an ideally finitealgebras Bilun, S.V. http://dspace.nbuv.gov.ua:80/handle/123456789/152370 2019-06-10T22:25:23Z 2007-01-01T00:00:00Z On sum of a nilpotent and an ideally finitealgebras Bilun, S.V. We study associative algebras R over arbitrary fields which can be decomposed into a sum R=A+B of their subalgebras A and B such that A²=0 and B is ideally finite (is a sum of its finite dimensional ideals). We prove that R has a locally nilpotent ideal I such that R/I is an extension of ideally finite algebra by a nilpotent algebra. Some properties of ideally finite algebras are also established. 2007-01-01T00:00:00Z Mathematics competition http://dspace.nbuv.gov.ua:80/handle/123456789/152369 2019-06-10T22:25:31Z 2007-01-01T00:00:00Z Mathematics competition The Shevchenko Scientific Society of America and U.S.-Ukraine Foundation are sponsoring an annual mathematics competition for young mathematicians in Ukraine. The winner of the competition will be awarded a prize of 5000 USD. The goal of the competition is to help young mathematicians who are working at research institutions in Ukraine, and to stimulate the interest of young people in pure and applied science. The competition is open to citizens of Ukraine who are working permanently in Ukraine, 35 years old, or younger, and who posses the degree of Kandydat, or D.Sc., in physico-mathematical sciences 2007-01-01T00:00:00Z