http://dspace.nbuv.gov.ua:80/handle/123456789/150384 2026-04-09T14:26:04Z http://dspace.nbuv.gov.ua:80/handle/123456789/153352 Effective ring Zabavsky, B.V.; Kuznitska, B.M. In this paper we will investigate commutative Bezout domains whose finite homomorphic images are semipotent rings. Among such commutative Bezout rings we consider a new class of rings and call them an effective rings. Furthermore we prove that effective rings are elementary divisor rings. 2014-01-01T00:00:00Z http://dspace.nbuv.gov.ua:80/handle/123456789/153351 Construction of free g-dimonoids Movsisyan, Yu.; Davidov, S.; Safaryan, M. In this paper, the concept of a g-dimonoid is introduced and the construction of a free g-dimonoid is described. (A g-dimonoid is a duplex satisfying two additional identities.) 2014-01-01T00:00:00Z http://dspace.nbuv.gov.ua:80/handle/123456789/153350 Matrix approach to noncommutative stably free modules and Hermite rings Lezama, O.; Gallego, C. In this paper we present a matrix-constructive proof of an Stafford’s Theorem about stably free modules over noncommutative rings. Matrix characterizations of noncommutative Hermite and projective-free rings are exhibit. Quotients, products and localizations of Hermite and some other classes of rings close related to Hermite rings are also considered. 2014-01-01T00:00:00Z http://dspace.nbuv.gov.ua:80/handle/123456789/153349 On graphs with graphic imbalance sequences Kozerenko, S.; Skochko, V. The imbalance of the edge e = uv in a graph G is the value imbG(e) = |dG(u) − dG(v)|. We prove that the sequence MG of all edge imbalances in G is graphic for several classes of graphs including trees, graphs in which all non-leaf vertices form a clique and the so-called complete extensions of paths, cycles and complete graphs. Also, we formulate two interesting conjectures related to graphicality of MG. 2014-01-01T00:00:00Z