American Mathematical Society TranslationsSeries 2 1993; 195 pp; hardcover Volume: 156 ISBN10: 0821875035 ISBN13: 9780821875032 List Price: US$125 Member Price: US$100 Order Code: TRANS2/156
 This book contains the doctoral dissertations of three students from Novosibirsk who participated in the seminar of L. A. Bokut'. The dissertation of Gerasimov focuses on Cohn's theory of noncommutative matrix localizations. Gerasimov presents a construction of matrix localization that is not directly related to (prime) matrix ideals of Cohn, but rather deals with localizations of arbitrary subsets of matrices over a ring. The work of Valitskas applies ideas and constructions of Gerasimov to embeddings of rings into radical rings (in the sense of Jacobson) to develop a theory essentially parallel to Cohn's theory of embeddings of rings into skew fields. Nesterenko's dissertation solves some important problems of Anan'in and Bergman about representations of (infinitedimensional) algebras and categories in (triangular) matrices over commutative rings. Readership Professional mathematicians, graduate students working in the theory of rings and its applications. Table of Contents Part I. Free associative algebras and inverting homomorphisms of rings  Introduction
 Free algebras and algebras with a single relation
 Inverting homomorphisms of rings
Part II. Representations of algebras by triangular matrices  Conventions and notation
 Introduction
 Representability of triangular categories and graded algebras
 Representation of algebras by triangular matrices. Algebras with diagonal
 Special representations of nilpotent graded algebras
 References
Part III. Embedding rings in radical rings and rational identities of radical algebras  Introduction
 Index of notation
 Absence of a finite basis of quasiidentities for the quasivariety of rings embeddable in radical rings
 Examples of noninvertible rings embeddable in groups
 Representation of finitedimensional Lie algebras in radical rings
 Rational identities of radical algebras
 References
