http://dspace.nbuv.gov.ua:80/handle/123456789/150398 2026-04-21T01:12:12Z http://dspace.nbuv.gov.ua:80/handle/123456789/155960 A criterion of elementary divisor domain for distributive domains Bokhonko, V.; Zabavsky, B.V. In this paper we introduce the notion of the neat range one for Bezout duo-domains. We show that a distributive Bezout domain is an elementary divisor domain if and only if it is a duo-domain of neat range one. 2017-01-01T00:00:00Z http://dspace.nbuv.gov.ua:80/handle/123456789/155938 Igor Rostislavovich Shafarevich (03.06.1923 -- 19.02.2017) Drozd, Yu.; Kirichenko, V.; Petravhuk, A.; Petrychkvych, V.; Shapochka, I.; Zabavskiy, B.; Zhuchok, A.; Varbanets, P. The great Russian mathematician Igor Rostislavovich Shafarevich died on February 19, 2017. This news grieved the whole mathematical society, since his name was inseparably linked to so many outstanding achievements and ideas of the modern mathematics, especially number theory and algebraic geometry. 2017-01-01T00:00:00Z http://dspace.nbuv.gov.ua:80/handle/123456789/155937 Dg algebras with enough idempotents, their dg modules and their derived categories Saorín, M. We develop the theory dg algebras with enough idempotents and their dg modules and show their equivalence with that of small dg categories and their dg modules. We introduce the concept of dg adjunction and show that the classical covariant tensor-Hom and contravariant Hom-Hom adjunctions of modules over associative unital algebras are extended as dg adjunctions between categories of dg bimodules. The corresponding adjunctions of the associated triangulated functors are studied, and we investigate when they are one-sided parts of bifunctors which are triangulated on both variables. We finally show that, for a dg algebra with enough idempotents, the perfect left and right derived categories are dual to each other. 2017-01-01T00:00:00Z http://dspace.nbuv.gov.ua:80/handle/123456789/155936 Equivalence of Carter diagrams Stekolshchik, R. We introduce the equivalence relation ρ on the set of Carter diagrams and construct an explicit transformation of any Carter diagram containing l-cycles with l>4 to an equivalent Carter diagram containing only 4-cycles. Transforming one Carter diagram Γ₁ to another Carter diagram Γ₂ we can get a certain intermediate diagram Γ′ which is not necessarily a Carter diagram. Such an intermediate diagram is called a connection diagram. The relation ρ is the equivalence relation on the set of Carter diagrams and connection diagrams. The properties of connection and Carter diagrams are studied in this paper. The paper contains an alternative proof of Carter's classification of admissible diagrams. 2017-01-01T00:00:00Z