Department of Algebra
Pidstryhach Institute for Applied Problems
of Mechanics and Mathematics
National Academy of Sciences of Ukraine
The book is devoted to investigation of arithmetic of the matrix rings over certain classes of commutative finitely generated principal ideals domains. We mainly concentrate on constructing of the matrix factorization theory. We reveal a close relationship between the matrix factorization and specific properties of ubgroups of the complete linear group and the special normal form of matrices with respect to unilateral equivalence. The properties of matrices over rings of stable range 1.5 are thoroughly studied.