**Translations of Mathematical Monographs**

1991;
81 pp;
Hardcover

MSC: Primary 16;
Secondary 08; 15

**Print ISBN: 978-0-8218-4548-6
Product Code: MMONO/87**

List Price: $41.00

Individual Member Price: $32.80

# Ideals of Identities of Associative Algebras

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*A.R. Kemer*

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.