Algebra and Discrete Mathematics, 2003, № 3http://dspace.nbuv.gov.ua:80/handle/123456789/1503282024-03-29T00:40:24Z2024-03-29T00:40:24ZGyrogroups and left gyrogroups as transversals of a special kindKuznetsov, E.http://dspace.nbuv.gov.ua:80/handle/123456789/1557282019-06-18T22:27:05Z2003-01-01T00:00:00ZGyrogroups and left gyrogroups as transversals of a special kind
Kuznetsov, E.
In this article we study gyrogroups and left gyrogroups as transversals in some suitable groups to its subgroups.
These objects were introduced into consideration in a connection
with an investigation of analogies between symmetries in the classical mechanics and in the relativistic one. The author introduce
some new notions into consideration (for example, a weak gyrotransversal) and give a full description of left gyrogroups (and gyrogroups) in terms of transversal identities. Also he generalize a
construction of a diagonal transversal and obtain a set of new examples of left gyrogroups.
2003-01-01T00:00:00ZOn equivalence of some subcategories of modules in Morita contextsKashu, A.I.http://dspace.nbuv.gov.ua:80/handle/123456789/1557272019-06-17T22:25:56Z2003-01-01T00:00:00ZOn equivalence of some subcategories of modules in Morita contexts
Kashu, A.I.
2003-01-01T00:00:00ZOn a group theoretical construction of expanding graphsUstimenko, V.A.http://dspace.nbuv.gov.ua:80/handle/123456789/1557042019-06-17T22:28:31Z2003-01-01T00:00:00ZOn a group theoretical construction of expanding graphs
Ustimenko, V.A.
2003-01-01T00:00:00ZOn the separability of the restriction functorTheohari-Apostolidi, Th.Vavatsoulas, H.http://dspace.nbuv.gov.ua:80/handle/123456789/1557032019-06-17T22:25:55Z2003-01-01T00:00:00ZOn the separability of the restriction functor
Theohari-Apostolidi, Th.; Vavatsoulas, H.
Let G be a group, Λ = L
σ∈G Λσ a strongly
graded ring by G, H a subgroup of G and ΛH =
L
σ∈H Λσ. We
give a necessary and sufficient condition for the ring Λ/ΛH to be
separable, generalizing the corresponding result for the ring extension Λ/Λ1. As a consequence of this result we give a condition for
Λ to be a hereditary order in case Λ is a strongly graded by finite
group R-order in a separable K-algebra, for R a Dedekind domain
with quotient field K.
2003-01-01T00:00:00Z