http://dspace.nbuv.gov.ua:80/handle/123456789/150390 2026-04-06T07:18:47Z http://dspace.nbuv.gov.ua:80/handle/123456789/155173 Quasi-Euclidean duo rings with elementary reduction of matrices Romaniv, O.; Sagan, A. We establish necessary and sufficient conditions under which a class of quasi-Euclidean duo rings coincides with a class of rings with elementary reduction of matrices. We prove that a Bezout duo ring with stable range 1 is a ring with elementary reduction of matrices. It is proved that a semiexchange quasi-duo Bezout ring is a ring with elementary reduction of matrices iff it is a duo ring. 2015-01-01T00:00:00Z http://dspace.nbuv.gov.ua:80/handle/123456789/155170 Free abelian dimonoids Zhuchok, Y. We construct a free abelian dimonoid and describe the least abelian congruence on a free dimonoid. Also we show that free abelian dimonoids are determined by their endomorphism semigroups. 2015-01-01T00:00:00Z http://dspace.nbuv.gov.ua:80/handle/123456789/155168 A morphic ring of neat range one Pihura, O.; Zabavsky, B. We show that a commutative ring R has neat range one if and only if every unit modulo principal ideal of a ring lifts to a neat element. We also show that a commutative morphic ring R has a neat range one if and only if for any elements a,b ∈ R such that aR=bR there exist neat elements s,t∈R such that bs=c, ct=b. Examples of morphic rings of neat range one are given. 2015-01-01T00:00:00Z http://dspace.nbuv.gov.ua:80/handle/123456789/155167 A Group-theoretic Approach to Covering Systems Jones, L.; White, D. In this article, we show how group actions can be used to examine the set of all covering systems of the integers with a fixed set of distinct moduli. 2015-01-01T00:00:00Z