Translations of Mathematical Monographs 1991; 81 pp; hardcover Volume: 87 ISBN10: 0821845489 ISBN13: 9780821845486 List Price: US$39 Member Price: US$31.20 Order Code: MMONO/87
 This book concerns the study of the structure of identities of PIalgebras over a field of characteristic zero. In the first chapter, the author brings out the connection between varieties of algebras and finitelygenerated superalgebras. The second chapter examines graded identities of finitelygenerated PIsuperalgebras. One of the results proved concerns the decomposition of Tideals, 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. Table of Contents  Varieties and Superalgebras
 Technical statements, utilizing the theory of representations of the symmetric group
 Grassmann hulls of superalgebras
 Semiprime varieties. Generalization of the DubnovIvanovNagataHigman theorem
 Identities of FinitelyGenerated Algebras
 Numerical characteristic of T\(_2\)ideals
 A theorem on the decomposition of T\(_2\)ideals
 Trace identities
 Graded identities of finitelygenerated superalgebras
 Solution of Specht's problem
 On asymptotic bases of identities
