Semirings and Affine Equations over Them: Theory and Applications

  • Jonathan S. Golan

Part of the Mathematics and Its Applications book series (MAIA, volume 556)

Table of contents

  1. Front Matter
    Pages i-xiii
  2. Jonathan S. Golan
    Pages 1-26
  3. Jonathan S. Golan
    Pages 27-38
  4. Jonathan S. Golan
    Pages 39-47
  5. Jonathan S. Golan
    Pages 49-57
  6. Jonathan S. Golan
    Pages 59-79
  7. Jonathan S. Golan
    Pages 81-99
  8. Jonathan S. Golan
    Pages 101-113
  9. Jonathan S. Golan
    Pages 115-127
  10. Jonathan S. Golan
    Pages 129-136
  11. Jonathan S. Golan
    Pages 137-149
  12. Jonathan S. Golan
    Pages 151-173
  13. Jonathan S. Golan
    Pages 175-190
  14. Back Matter
    Pages 191-241

About this book


Semiring theory stands with a foot in each of two mathematical domains. The first being abstract algebra and the other the fields of applied mathematics such as optimization theory, the theory of discrete-event dynamical systems, automata theory, and formal language theory, as well as from the allied areas of theoretical computer science and theoretical physics. Most important applications of semiring theory in these areas turn out to revolve around the problem of finding the equalizer of a pair of affine maps between two semimodules. In this volume, we chart the state of the art on solving this problem, and present many specific cases of applications.

This book is essentially the third part of a trilogy, along with Semirings and their Applications, and Power Algebras over Semirings, both written by the same author and published by Kluwer Academic Publishers in 1999. While each book can be read independently of the others, to get the full force of the theory and applications one should have access to all three.

This work will be of interest to academic and industrial researchers and graduate students. The intent of the book is to bring the applications to the attention of the abstract mathematicians and to make the abstract mathematics available to those who are using these tools in an ad-hoc manner without realizing the full force of the theory.


Abstract algebra algebra automata automata theory computer computer science dynamische Systeme equalizer formal language homomorphism optimization ring theory theoretical computer science

Authors and affiliations

  • Jonathan S. Golan
    • 1
  1. 1.Department of MathematicsUniversity of HaifaHaifaIsrael

Bibliographic information

  • DOI
  • Copyright Information Springer Science+Business Media B.V. 2003
  • Publisher Name Springer, Dordrecht
  • eBook Packages Springer Book Archive
  • Print ISBN 978-90-481-6310-6
  • Online ISBN 978-94-017-0383-3
  • Buy this book on publisher's site