Advertisement

Polynomial Identity Rings

  • Vesselin Drensky
  • Edward Formanek

Part of the Advanced Courses in Mathematics CRM Barcelona book series (ACMBIRK)

Table of contents

  1. Front Matter
    Pages i-vii
  2. Combinatorial Aspects in PI-Rings

    1. Front Matter
      Pages 1-1
    2. Vesselin Drensky, Edward Formanek
      Pages 3-4
    3. Vesselin Drensky, Edward Formanek
      Pages 5-18
    4. Vesselin Drensky, Edward Formanek
      Pages 19-35
    5. Vesselin Drensky, Edward Formanek
      Pages 37-47
    6. Vesselin Drensky, Edward Formanek
      Pages 49-58
    7. Vesselin Drensky, Edward Formanek
      Pages 59-74
    8. Vesselin Drensky, Edward Formanek
      Pages 75-86
    9. Vesselin Drensky, Edward Formanek
      Pages 87-101
    10. Vesselin Drensky, Edward Formanek
      Pages 103-117
    11. Vesselin Drensky, Edward Formanek
      Pages 119-130
  3. Polynomial Identity Rings

    1. Front Matter
      Pages 131-131
    2. Vesselin Drensky, Edward Formanek
      Pages 133-136
    3. Vesselin Drensky, Edward Formanek
      Pages 137-142
    4. Vesselin Drensky, Edward Formanek
      Pages 143-146
    5. Vesselin Drensky, Edward Formanek
      Pages 147-150
    6. Vesselin Drensky, Edward Formanek
      Pages 151-154
    7. Vesselin Drensky, Edward Formanek
      Pages 155-158
    8. Vesselin Drensky, Edward Formanek
      Pages 159-160
    9. Vesselin Drensky, Edward Formanek
      Pages 161-162
    10. Vesselin Drensky, Edward Formanek
      Pages 163-167
    11. Vesselin Drensky, Edward Formanek
      Pages 169-171
    12. Vesselin Drensky, Edward Formanek
      Pages 173-176
    13. Vesselin Drensky, Edward Formanek
      Pages 177-178
    14. Vesselin Drensky, Edward Formanek
      Pages 179-181
    15. Vesselin Drensky, Edward Formanek
      Pages 183-184
    16. Vesselin Drensky, Edward Formanek
      Pages 185-187
    17. Vesselin Drensky, Edward Formanek
      Pages 189-191
    18. Vesselin Drensky, Edward Formanek
      Pages 193-196
  4. Back Matter
    Pages 197-200

About this book

Introduction

A ring R satisfies a polynomial identity if there is a polynomial f in noncommuting variables which vanishes under substitutions from R. For example, commutative rings satisfy the polynomial f(x,y) = xy - yx and exterior algebras satisfy the polynomial f(x,y,z) = (xy - yx)z - z(xy - yx). "Satisfying a polynomial identity" is often regarded as a generalization of commutativity.

These lecture notes treat polynomial identity rings from both the combinatorial and structural points of view. The former studies the ideal of polynomial identities satisfied by a ring R. The latter studies the properties of rings which satisfy a polynomial identity.

The greater part of recent research in polynomial identity rings is about combinatorial questions, and the combinatorial part of the lecture notes gives an up-to-date account of recent research. On the other hand, the main structural results have been known for some time, and the emphasis there is on a presentation accessible to newcomers to the subject.

The intended audience is graduate students in algebra, and researchers in algebra, combinatorics and invariant theory.

Keywords

Combinatorics Commutative Algebras Finite Dimensional Algebras Polynomial Identity Algebras Polynomial Identity Rings

Authors and affiliations

  • Vesselin Drensky
    • 1
  • Edward Formanek
    • 2
  1. 1.Institute of Mathematics and InformaticsBulgarian Academy of SciencesBulgaria
  2. 2.Department of MathematicsPennsylvania State UniversityUSA

Bibliographic information