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Hardcover ISBN:  9780821875032 
Product Code:  TRANS2/156 
List Price:  $175.00 
MAA Member Price:  $157.50 
AMS Member Price:  $140.00 
eBook ISBN:  9781470433673 
Product Code:  TRANS2/156.E 
List Price:  $165.00 
MAA Member Price:  $148.50 
AMS Member Price:  $132.00 
Hardcover ISBN:  9780821875032 
eBook ISBN:  9781470433673 
Product Code:  TRANS2/156.B 
List Price:  $340.00 $257.50 
MAA Member Price:  $306.00 $231.75 
AMS Member Price:  $272.00 $206.00 

Book DetailsAmerican Mathematical Society Translations  Series 2Volume: 156; 1993; 195 ppMSC: Primary 16
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.
ReadershipProfessional mathematicians, graduate students working in the theory of rings and its applications.

Table of Contents

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

Introduction

Free algebras and algebras with a single relation

Inverting homomorphisms of rings

References

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

Conventions and Notation

Introduction

Representability of Triangular Categories and Graded Algebras

Representation of Algebras by Triangular Matrices. Algebras with Diagonal

Introduction

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

Absence of a Finite Basis of Quasiidentities for the Quasivariety of Rings Embeddable in Radivasl Rings

Examples of Noninvertible Rings Embeddable in Groups

Representation of FiniteDimensional Lie Algebras in Radical Rings

Rational Identities of Radical Algebras

References


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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.
Professional mathematicians, graduate students working in the theory of rings and its applications.

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

Introduction

Free algebras and algebras with a single relation

Inverting homomorphisms of rings

References

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

Conventions and Notation

Introduction

Representability of Triangular Categories and Graded Algebras

Representation of Algebras by Triangular Matrices. Algebras with Diagonal

Introduction

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

Absence of a Finite Basis of Quasiidentities for the Quasivariety of Rings Embeddable in Radivasl Rings

Examples of Noninvertible Rings Embeddable in Groups

Representation of FiniteDimensional Lie Algebras in Radical Rings

Rational Identities of Radical Algebras

References