Shchedryk V.P. Arithmetic of matrices over rings

Kyiv: Akademperiodyka, 2021. — 278 p. — ISBN 9789663604305.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 subgroups 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. The book is intended for experts in the ring theory and linear algebra, senior and post-graduate students.Preface.
Bezout rings and matrices over them.
Elementary divisor rings.
Llinear algebra technique in matrix rings.
Divisibility and associativity of matrices.
Factorization of matrices.
Invariants of primitive matrices with respect to Zelisko group action.
One-sided equivalence of matrices.
Notational conventions.
Bibliography.True PDF