Three papers on algebras and their representations
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Bibliographic Information
Three papers on algebras and their representations
(American Mathematical Society translations, Series 2,
American Mathematical Society, c1993
- Other Title
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3 papers on algebras and their representations
Available at 54 libraries
  Aomori
  Iwate
  Miyagi
  Akita
  Yamagata
  Fukushima
  Ibaraki
  Tochigi
  Gunma
  Saitama
  Chiba
  Tokyo
  Kanagawa
  Niigata
  Toyama
  Ishikawa
  Fukui
  Yamanashi
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  Aichi
  Mie
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  Yamaguchi
  Tokushima
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  Ehime
  Kochi
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Note
Includes bibliographical references
Description and Table of Contents
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 Ananin and Bergman about representations of (infinite-dimensional) algebras and categories in (triangular) matrices over commutative rings.
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 quasi-identities for the quasi-variety of rings embeddable in radical rings Examples of noninvertible rings embeddable in groups Representation of finite-dimensional Lie algebras in radical rings Rational identities of radical algebras References.
by "Nielsen BookData"