This book concerns the study of the structure of identities of PI-algebras over a field of characteristic zero. In the first chapter, the author brings out the connection between varieties of algebras and finitely-generated superalgebras. The second chapter examines graded identities of finitely-generated PI-superalgebras. One of the results proved concerns the decomposition of T-ideals, which is very useful for the study of specific varieties. In the fifth section of Chapter Two, the author solves Specht's problem, which asks whether every associative algebra over a field of characteristic zero has a finite basis of identities. The book closes with an application of methods and results established earlier: the author finds asymptotic bases of identities of algebras with unity satisfying all of the identities of the full algebra of matrices of order two.
Author(s): Aleksandr Robertovich Kemer
Series: Translations of Mathematical Monographs, Vol. 87
Publisher: American Mathematical Society
Year: 1991
Language: English
Pages: C+vi+81+B
Cover
S Title
Ideals of Identities of Associative Algebras
Copyright ©1991 by the American Mathematical Society
ISBN 0-8218-4548-9
QA251.5.K4613 1991 512' .24-dc20
LCCN 91-8147
Contents
Introduction
CHAPTER I Varieties and Superalgebras
§ 1. Technical statements, utilizing the theory of representations of the symmetric group
§2. Grassmann hulls of superalgebras
§3. Semiprime varieties. Generalization of the Dubnov-Ivanov-Nagata-Higman theorem
CHAPTER II Identities of Finitely-Generated Algebras
§1. Numerical characteristics of T2-ideals
§2. A theorem on the decomposition of T2-ideals
§3. Trace identities
§4. Graded identities of finitely-generated superalgebras
§5. Solution of Specht's problem
§6. On asymptotic bases of identities
Bibliography
Subject Index
Back Cover
