Romaniv O. Rings of elementary divisors and related algebraic structures

The dissertation is devoted to investigation of rings of elementary divisors, more precisely, to their partial case - rings with elementary reduction of matrices. Some new classes of commutative as well as non-commutative rings with elementary reduction of matrices are found. We establish some properties of non-commutative elementary principal rings and one-sided w-Euclidean rings with their subsequent investigation on the possibility of elementary reduction of matrices. We investigate Bezout rings and 2-Euclidean rings in which any maximally non-principal right ideal is two-sided; in these classes we describe rings which admit elementary reduction of matrices. Key words: Bezout ring, elementary divisors ring, ring with elementary reduction of matrices, duo ring, maximal nonprincipal right ideal.