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Three Papers on Algebras and Their Representations
 
Three Papers on Algebras and Their Representations
Hardcover ISBN:  978-0-8218-7503-2
Product Code:  TRANS2/156
List Price: $175.00
MAA Member Price: $157.50
AMS Member Price: $140.00
eBook ISBN:  978-1-4704-3367-3
Product Code:  TRANS2/156.E
List Price: $165.00
MAA Member Price: $148.50
AMS Member Price: $132.00
Hardcover ISBN:  978-0-8218-7503-2
eBook: ISBN:  978-1-4704-3367-3
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
Three Papers on Algebras and Their Representations
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Three Papers on Algebras and Their Representations
Hardcover ISBN:  978-0-8218-7503-2
Product Code:  TRANS2/156
List Price: $175.00
MAA Member Price: $157.50
AMS Member Price: $140.00
eBook ISBN:  978-1-4704-3367-3
Product Code:  TRANS2/156.E
List Price: $165.00
MAA Member Price: $148.50
AMS Member Price: $132.00
Hardcover ISBN:  978-0-8218-7503-2
eBook ISBN:  978-1-4704-3367-3
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 Details
     
     
    American Mathematical Society Translations - Series 2
    Volume: 1561993; 195 pp
    MSC: 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 (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
     
     
    • 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 Quasi-identities for the Quasivariety of Rings Embeddable in Radivasl Rings
    • Examples of Noninvertible Rings Embeddable in Groups
    • Representation of Finite-Dimensional Lie Algebras in Radical Rings
    • Rational Identities of Radical Algebras
    • References
  • Requests
     
     
    Review Copy – for publishers of book reviews
    Permission – for use of book, eBook, or Journal content
    Accessibility – to request an alternate format of an AMS title
Volume: 1561993; 195 pp
MSC: 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 (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.

  • 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 Quasi-identities for the Quasivariety of Rings Embeddable in Radivasl Rings
  • Examples of Noninvertible Rings Embeddable in Groups
  • Representation of Finite-Dimensional Lie Algebras in Radical Rings
  • Rational Identities of Radical Algebras
  • References
Review Copy – for publishers of book reviews
Permission – for use of book, eBook, or Journal content
Accessibility – to request an alternate format of an AMS title
Please select which format for which you are requesting permissions.