Shchedryk V. Factorization and one-sided equivalence of matrices over commutative elementary divisor domains

In this thesis we propose a matrices factorization theory over commutative elementary divisor domains based on an analysis of the relationship of certain subsets and subgroups of the general linear group. It is shown that the problem of description of nonassociative divisors of matrices can be reduced to constructing some normal form of matrices with respect to one-sided transformation of the form РФ where Р is an invertible matrix and Ф is a d -matrix. We describe the basic invariants of matrices with respect to such transformations and, in some cases, we obtain an explicit description of such form. The results are applied to the study of properties of elements in commutative elementary divisor domains.