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Three Papers on Algebras and Their Representations : American Mathematical Society Translations - V. N. Gerasimov

Three Papers on Algebras and Their Representations

American Mathematical Society Translations

Hardcover ISBN: 9780821875032
Number Of Pages: 195

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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 (infinite-dimensional) algebras and categories in (triangular) matrices over commutative rings.

Free associative algebras and inverting homomorphisms of rings: Introduction
Free algebras and algebras with a single relation
Inverting homomorphisms of rings
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
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
Table of Contents provided by Publisher. All Rights Reserved.

ISBN: 9780821875032
ISBN-10: 0821875035
Series: American Mathematical Society Translations : Book 156
Audience: Professional
Format: Hardcover
Language: English
Number Of Pages: 195
Publisher: American Mathematical Society
Country of Publication: US
Dimensions (cm): 26.67 x 18.42  x 1.91
Weight (kg): 0.57

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