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.

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 Dubnov-Ivanov-Nagata-Higman theorem
• Identities of Finitely-Generated Algebras
• Numerical characteristic of T\(_2\)-ideals
• A theorem on the decomposition of T\(_2\)-ideals
• Trace identities
• Graded identities of finitely-generated superalgebras
• Solution of Specht's problem
• On asymptotic bases of identities