Three Papers on Algebras and Their Representations (156) (AMERICAN MATHEMATICAL SOCIETY TRANSLATIONS SERIES 2) - Hardcover

Gerasimov, V. N.; Nesterenko, N. G.; Valitskas, A. I.

9780821875032: Three Papers on Algebras and Their Representations (156) (AMERICAN MATHEMATICAL SOCIETY TRANSLATIONS SERIES 2)

Hardcover

ISBN 10: 0821875035 ISBN 13: 9780821875032

Publisher: Amer Mathematical Society, 1993

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.

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Language Notes:

Text: English (translation)
Original Language: Russian

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