Algebra and Discrete Mathematics, 2016, Vol. 21, № 1http://dspace.nbuv.gov.ua:80/handle/123456789/1503932026-04-15T04:35:59Z2026-04-15T04:35:59ZOn nilpotent Lie algebras of derivations with large centerSysak, K.http://dspace.nbuv.gov.ua:80/handle/123456789/1552122019-06-16T22:26:21Z2016-01-01T00:00:00ZOn 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.
2016-01-01T00:00:00ZThe groups whose cyclic subgroups are either ascendant or almost self-normalizingKurdachenko, L.A.Pypka, A.A.Semko, N.N.http://dspace.nbuv.gov.ua:80/handle/123456789/1552082019-06-16T22:28:08Z2016-01-01T00:00:00ZThe 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.
2016-01-01T00:00:00ZA survey of results on radicals and torsions in modulesKashu, A.I.http://dspace.nbuv.gov.ua:80/handle/123456789/1552072019-06-16T22:27:11Z2016-01-01T00:00:00ZA 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.
2016-01-01T00:00:00ZConstruction of self-dual binary [2²ⁿ,2²ⁿ⁻¹,2ⁿ]-codesHannusch, C.Lakatos, P.http://dspace.nbuv.gov.ua:80/handle/123456789/1552032019-06-16T22:26:53Z2016-01-01T00:00:00ZConstruction 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.
2016-01-01T00:00:00Z