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Power Algebras over Semirings

With Applications in Mathematics and Computer Science

  • Jonathan S. Golan

Part of the Mathematics and Its Applications book series (MAIA, volume 488)

Table of contents

  1. Front Matter
    Pages i-x
  2. Jonathan S. Golan
    Pages 1-5
  3. Jonathan S. Golan
    Pages 7-26
  4. Jonathan S. Golan
    Pages 27-35
  5. Jonathan S. Golan
    Pages 37-59
  6. Jonathan S. Golan
    Pages 61-66
  7. Jonathan S. Golan
    Pages 67-88
  8. Jonathan S. Golan
    Pages 89-112
  9. Jonathan S. Golan
    Pages 113-139
  10. Jonathan S. Golan
    Pages 141-154
  11. Jonathan S. Golan
    Pages 155-167
  12. Back Matter
    Pages 169-206

About this book

Introduction

This monograph is a continuation of several themes presented in my previous books [146, 149]. In those volumes, I was concerned primarily with the properties of semirings. Here, the objects of investigation are sets of the form RA, where R is a semiring and A is a set having a certain structure. The problem is one of translating that structure to RA in some "natural" way. As such, it tries to find a unified way of dealing with diverse topics in mathematics and theoretical com­ puter science as formal language theory, the theory of fuzzy algebraic structures, models of optimal control, and many others. Another special case is the creation of "idempotent analysis" and similar work in optimization theory. Unlike the case of the previous work, which rested on a fairly established mathematical foundation, the approach here is much more tentative and docimastic. This is an introduction to, not a definitative presentation of, an area of mathematics still very much in the making. The basic philosphical problem lurking in the background is one stated suc­ cinctly by Hahle and Sostak [185]: ". . . to what extent basic fields of mathematics like algebra and topology are dependent on the underlying set theory?" The conflicting definitions proposed by various researchers in search of a resolution to this conundrum show just how difficult this problem is to see in a proper light.

Keywords

Algebraic structure Mathematica algebra computer computer science dynamische Systeme formal language set theory sets

Authors and affiliations

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

Bibliographic information

  • DOI https://doi.org/10.1007/978-94-015-9241-3
  • Copyright Information Springer Science+Business Media B.V. 1999
  • Publisher Name Springer, Dordrecht
  • eBook Packages Springer Book Archive
  • Print ISBN 978-90-481-5270-4
  • Online ISBN 978-94-015-9241-3
  • Buy this book on publisher's site