Algebra and Discrete Mathematics, 2003, Vol. 2 http://dspace.nbuv.gov.ua:80/handle/123456789/150325 2026-04-18T12:15:31Z 2026-04-18T12:15:31Z Gyrogroups and left gyrogroups as transversals of a special kind Kuznetsov, E. http://dspace.nbuv.gov.ua:80/handle/123456789/155728 2019-06-18T22:27:05Z 2003-01-01T00:00:00Z Gyrogroups 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. 2003-01-01T00:00:00Z On equivalence of some subcategories of modules in Morita contexts Kashu, A.I. http://dspace.nbuv.gov.ua:80/handle/123456789/155727 2019-06-17T22:25:56Z 2003-01-01T00:00:00Z On equivalence of some subcategories of modules in Morita contexts Kashu, A.I. 2003-01-01T00:00:00Z On faithful actions of groups and semigroups by orientation-preserving plane isometries Vorobets, Y. http://dspace.nbuv.gov.ua:80/handle/123456789/155725 2019-06-17T22:28:39Z 2003-01-01T00:00:00Z On faithful actions of groups and semigroups by orientation-preserving plane isometries Vorobets, Y. Feitful representations of two generated free groups and free semigroups by orientation-preserving plane isometries constructed. 2003-01-01T00:00:00Z Binary coronas of balleans Protasov, I.V. http://dspace.nbuv.gov.ua:80/handle/123456789/155724 2019-06-17T22:25:57Z 2003-01-01T00:00:00Z Binary coronas of balleans Protasov, I.V. A ballean B is a set X endowed with some family of subsets of X which are called the balls. We postulate the properties of the family of balls in such a way that a ballean can be considered as an asymptotic counterpart of a uniform topological space. Using slow oscillating functions from X to {0, 1}, we define a zero-dimensional compact space which is called a binary corona of B. We define a class of binary normal ballean and, for every ballean from this class, give an intrinsic characterization of its binary corona. The class of binary normal balleans contains all balleans of graph. We show that a ballean of graph is a projective limit of some sequence of C˘ech-Stone compactifications of discrete spaces. The obtained results witness that a binary corona of balleans can be interpreted as a "generalized space of ends" of ballean. 2003-01-01T00:00:00Z