http://dspace.nbuv.gov.ua:80/handle/123456789/150393 Wed, 15 Apr 2026 06:08:18 GMT 2026-04-15T06:08:18Z http://dspace.nbuv.gov.ua:80/bitstream/id/472622/ http://dspace.nbuv.gov.ua:80/handle/123456789/150393 http://dspace.nbuv.gov.ua:80/handle/123456789/155212 On nilpotent Lie algebras of derivations with large center Sysak, K. Let K be a field of characteristic zero and A an associative commutative K-algebra that is an integral domain. Denote by R the quotient field of A and by W(A)=RDerA the Lie algebra of derivations on R that are products of elements of R and derivations on A. Nilpotent Lie subalgebras of the Lie algebra W(A) of rank n over R with the center of rank n−1 are studied. It is proved that such a Lie algebra L is isomorphic to a subalgebra of the Lie algebra un(F) of triangular polynomial derivations where F is the field of constants for L. Fri, 01 Jan 2016 00:00:00 GMT http://dspace.nbuv.gov.ua:80/handle/123456789/155212 2016-01-01T00:00:00Z http://dspace.nbuv.gov.ua:80/handle/123456789/155208 The groups whose cyclic subgroups are either ascendant or almost self-normalizing Kurdachenko, L.A.; Pypka, A.A.; Semko, N.N. The main result of this paper shows a description of locally finite groups, whose cyclic subgroups are either almost self-normalizing or ascendant. Also, we obtained some natural corollaries of the above situation. Fri, 01 Jan 2016 00:00:00 GMT http://dspace.nbuv.gov.ua:80/handle/123456789/155208 2016-01-01T00:00:00Z http://dspace.nbuv.gov.ua:80/handle/123456789/155207 A survey of results on radicals and torsions in modules Kashu, A.I. In this work basic results of the author on radicals in module categories are presented in a short form. Principal topics are: types of preradicals and their characterizations; classes of R-modules and sets of left ideals of R; notions and constructions associated to radicals; rings of quotients and localizations; preradicals in adjoint situation; torsions in Morita contexts; duality between localizations and colocalizations; principal functors and preradicals; special classes of modules; preradicals and operations in the lattices of submodules; closure operators and preradicals. Fri, 01 Jan 2016 00:00:00 GMT http://dspace.nbuv.gov.ua:80/handle/123456789/155207 2016-01-01T00:00:00Z http://dspace.nbuv.gov.ua:80/handle/123456789/155203 Construction of self-dual binary [2²ⁿ,2²ⁿ⁻¹,2ⁿ]-codes Hannusch, C.; Lakatos, P. The binary Reed-Muller code RM(m−n,m) corresponds to the n-th power of the radical of GF(2)[G], where G is an elementary abelian group of order 2m. Self-dual RM-codes (i.e. some powers of the radical of the previously mentioned group algebra) exist only for odd m. The group algebra approach enables us to find a self-dual code for even m=2n in the radical of the previously mentioned group algebra with similarly good parameters as the self-dual RM codes. Fri, 01 Jan 2016 00:00:00 GMT http://dspace.nbuv.gov.ua:80/handle/123456789/155203 2016-01-01T00:00:00Z