Three Papers on Algebras and Their Representations ( American Mathematical Society Translations - Series 2 )

Publication series ：American Mathematical Society Translations - Series 2

Author： V. N. Gerasimov;N. G. Nesterenko;A. I. Valitskas  

Publisher： American Mathematical Society‎

Publication year： 1993

E-ISBN: 9781470433673

P-ISBN(Hardback):  9780821875032

Subject： O151 theory of algebraic equations, linear algebra

Keyword： 暂无分类

Language： ENG

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Three Papers on Algebras and Their Representations

Description

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.

Chapter

Cover

Title page

Contents

Foreword

Free Associative Algebras and Inverting Homomorphisms of Rings by V. Gerasimov

Introduction

Chapter 1. Free algebras and algebras with a single relation

Chapter 2. Inverting homomorphisms of rings

References

Part II. Representations of Algebras by Triangular Matrices by N. Nesterenko

Conventions and Notation

Introduction

Chapter 1. Representability of Triangular Categories and Graded Algebras

Chapter 2. Representation of Algebras by Triangular Matrices. Algebras with Diagonal

Introduction

Chapter 3. Special Representations of Nilpotent Graded Algebras

References

Part III. Embedding rings in radical rings and rational identities of radical algebras by Valitskas, A

Introduction

Index of Notation

Chapter 1. Absence of a Finite Basis of Quasi-identities for the Quasivariety of Rings Embeddable in Radivasl Rings

Chapter 2. Examples of Noninvertible Rings Embeddable in Groups

Chapter 3. Representation of Finite-Dimensional Lie Algebras in Radical Rings

Chapter 4. Rational Identities of Radical Algebras

References

Back Cover

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