**American Mathematical Society Translations - Series 2**

1993;
195 pp;
Hardcover

MSC: Primary 16;

Print ISBN: 978-0-8218-7503-2

Product Code: TRANS2/156

List Price: $125.00

Individual Member Price: $100.00

**Electronic ISBN: 978-1-4704-3367-3
Product Code: TRANS2/156.E**

List Price: $125.00

Individual Member Price: $100.00

# Three Papers on Algebras and Their Representations

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*V. N. Gerasimov; N. G. Nesterenko; A. I. Valitskas*

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 (infinite-dimensional) 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

## Three Papers on Algebras and Their Representations

- Cover Cover11
- Title page v6
- Contents vii8
- Foreword ix10
- Free Associative Algebras and Inverting Homomorphisms of Rings by V. Gerasimov 112
- Introduction 314
- Chapter 1. Free algebras and algebras with a single relation 920
- Chapter 2. Inverting homomorphisms of rings 5162
- References 7586
- Part II. Representations of Algebras by Triangular Matrices by N. Nesterenko 7788
- Conventions and Notation 7990
- Introduction 8192
- Chapter 1. Representability of Triangular Categories and Graded Algebras 8798
- Chapter 2. Representation of Algebras by Triangular Matrices. Algebras with Diagonal 99110
- Introduction 8192
- Chapter 3. Special Representations of Nilpotent Graded Algebras 117128
- References 124135
- Part III. Embedding rings in radical rings and rational identities of radical algebras by Valitskas, A 125136
- Introduction 127138
- Index of Notation 137148
- Chapter 1. Absence of a Finite Basis of Quasi-identities for the Quasivariety of Rings Embeddable in Radivasl Rings 139150
- Chapter 2. Examples of Noninvertible Rings Embeddable in Groups 157168
- Chapter 3. Representation of Finite-Dimensional Lie Algebras in Radical Rings 177188
- Chapter 4. Rational Identities of Radical Algebras 183194
- References 194205
- Back Cover Back Cover1210