http://dspace.nbuv.gov.ua:80/handle/123456789/150407 Mon, 20 Apr 2026 06:20:59 GMT 2026-04-20T06:20:59Z http://dspace.nbuv.gov.ua:80/bitstream/id/448192/ http://dspace.nbuv.gov.ua:80/handle/123456789/150407 http://dspace.nbuv.gov.ua:80/handle/123456789/188496 Free ultra-groups, generators and relations Tolue, B.; Zolfaghari, P.; Moghaddasi, Gh. In this paper, we intend to define an ultra-group by its presentation. The attitude of the presentation for a group was the key for us to investigate in this area. Instead of writing whole elements of an ultra-group, we denote it by its generators and the relations among those generators. A general computational approach for finitely presented ultra-groups by quotient ultra-groups and subultra-groups is described and some examples are presented. It is the way that can clarify the structure of an ultra-group quicker than having just a list of elements. Tue, 01 Jan 2019 00:00:00 GMT http://dspace.nbuv.gov.ua:80/handle/123456789/188496 2019-01-01T00:00:00Z http://dspace.nbuv.gov.ua:80/handle/123456789/188495 The sparing number of the powers of certain Mycielski graphs Sudev, N.K.; Chithra, K.P.; Germina, K.A. In this paper, we discuss the sparing number of the power graphs of the Mycielski graphs of certain graph classes. Tue, 01 Jan 2019 00:00:00 GMT http://dspace.nbuv.gov.ua:80/handle/123456789/188495 2019-01-01T00:00:00Z http://dspace.nbuv.gov.ua:80/handle/123456789/188494 On NSP constants of a matrix and their linear preservers Skrzyński, M. We collect some basic properties of NSP constants of a matrix, discuss an additive behavior of the spark, and prove two theorems characterizing linear endomorphisms which preserve the NSP constants. Tue, 01 Jan 2019 00:00:00 GMT http://dspace.nbuv.gov.ua:80/handle/123456789/188494 2019-01-01T00:00:00Z http://dspace.nbuv.gov.ua:80/handle/123456789/188493 Adjoint functors, preradicals and closure operators in module categories Kashu, A.I. In this article preradicals and closure operators are studied in an adjoint situation, defined by two covariant functors between the module categories R-Mod and S-Mod. The mappings which determine the relationship between the classes of preradicals and the classes of closure operators of these categories are investigated. The goal of research is to elucidate the concordance (compatibility) of these mappings. For that some combinations of them, consisting of four mappings, are considered and the commutativity of corresponding diagrams (squares) is studied. The obtained results show the connection between considered mappings in adjoint situation. Tue, 01 Jan 2019 00:00:00 GMT http://dspace.nbuv.gov.ua:80/handle/123456789/188493 2019-01-01T00:00:00Z