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Semirings and their Applications

  • Book
  • © 1999

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Authors:
  1. Jonathan S. Golan

    1. University of Haifa, Haifa, Israël

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Table of contents (25 chapters)

  1. Front Matter

    Pages i-xi
    Download chapter PDF

  2. Hemirings and Semirings: Definitions and Examples

    • Jonathan S. Golan
    Pages 1-18

  3. Sets and Relations with Values in a Semiring

    • Jonathan S. Golan
    Pages 19-25

  4. Building New Semirings from Old

    • Jonathan S. Golan
    Pages 27-42

  5. Some Conditions on Semirings

    • Jonathan S. Golan
    Pages 43-57

  6. Complemented Elements in Semirings

    • Jonathan S. Golan
    Pages 59-63

  7. Ideals in Semirings

    • Jonathan S. Golan
    Pages 65-83

  8. Prime and Semiprime Ideals in Semirings

    • Jonathan S. Golan
    Pages 85-94

  9. Factor Semirings

    • Jonathan S. Golan
    Pages 95-103

  10. Morphisms of Semirings

    • Jonathan S. Golan
    Pages 105-120

  11. Kernels of Morphisms

    • Jonathan S. Golan
    Pages 121-127

  12. Semirings of Fractions

    • Jonathan S. Golan
    Pages 129-134

  13. Euclidean Semirings

    • Jonathan S. Golan
    Pages 135-141

  14. Additively-Regular Semirings

    • Jonathan S. Golan
    Pages 143-147

  15. Semimodules over Semirings

    • Jonathan S. Golan
    Pages 149-161

  16. Factor Semimodules

    • Jonathan S. Golan
    Pages 163-179

  17. Some Constructions for Semimodules

    • Jonathan S. Golan
    Pages 181-190

  18. Free, Projective, and Injective Semimodules

    • Jonathan S. Golan
    Pages 191-202

  19. Localization of Semimodules

    • Jonathan S. Golan
    Pages 203-210

  20. Linear Algebra over a Semiring

    • Jonathan S. Golan
    Pages 211-221
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Keywords

About this book

There is no branch of mathematics, however abstract, which may not some day be applied to phenomena of the real world. - Nikolai Ivanovich Lobatchevsky This book is an extensively-revised and expanded version of "The Theory of Semirings, with Applicationsin Mathematics and Theoretical Computer Science" [Golan, 1992], first published by Longman. When that book went out of print, it became clear - in light of the significant advances in semiring theory over the past years and its new important applications in such areas as idempotent analysis and the theory of discrete-event dynamical systems - that a second edition incorporating minor changes would not be sufficient and that a major revision of the book was in order. Therefore, though the structure of the first «dition was preserved, the text was extensively rewritten and substantially expanded. In particular, references to many interesting and applications of semiring theory, developed in the past few years, had to be added. Unfortunately, I find that it is best not to go into these applications in detail, for that would entail long digressions into various domains of pure and applied mathematics which would only detract from the unity of the volume and increase its length considerably. However, I have tried to provide an extensive collection of examples to arouse the reader's interest in applications, as well as sufficient citations to allow the interested reader to locate them. For the reader's convenience, an index to these citations is given at the end of the book .

Authors and Affiliations

  • University of Haifa, Haifa, Israël

    Jonathan S. Golan

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