AMS Bookstore LOGO amslogo
Return to List

AMS TextbooksAMS Applications-related Books

Ideals of Identities of Associative Algebras
Aleksandr Robertovich Kemer

Translations of Mathematical Monographs
1991; 81 pp; hardcover
Volume: 87
ISBN-10: 0-8218-4548-9
ISBN-13: 978-0-8218-4548-6
List Price: US$41
Member Price: US$32.80
Order Code: MMONO/87
[Add Item]

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
Powered by MathJax

  AMS Home | Comments:
© Copyright 2014, American Mathematical Society
Privacy Statement

AMS Social

AMS and Social Media LinkedIn Facebook Podcasts Twitter YouTube RSS Feeds Blogs Wikipedia