Semirings and their applications

Bibliographic Information

Semirings and their applications

by Jonathan S. Golan

Kluwer Academic Publishers, c1999

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Note

Includes bibliographical references (p. [307]-354) and index

Description and Table of Contents

Description

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 .

Table of Contents

Preface. 1. Hemirings and semirings: definitions and examples. 2. Sets and relations with values in a semiring. 3. Building new semirings from old. 4. Some conditions on semirings. 5. Complemented elements in semirings. 6. Ideals in semirings. 7. Prime and semiprime ideals in semirings. 8. Factor semirings. 9. Morphisms of semirings. 10. Kernels of morphisms. 11. Semirings of fractions. 12. Euclidean semirings. 13. Additively-regular semirings. 14. Semimodules over semirings. 15. Factor semimodules. 16. Some constructions for semimodules. 17. Free, projective, and injective semimodules. 18. Localization of semimodules. 19. Linear algebra over a semiring. 20. Partially-ordered semirings. 21. Lattice-ordered semirings. 22. Complete semirings. 23. Complete semimodules. 24. CLO-semirings. 25. Fixed points of affine maps. References. Index of applications. Index of terminology.

by "Nielsen BookData"

Details

  • NCID
    BA80040804
  • ISBN
    • 0792357868
  • LCCN
    99015356
  • Country Code
    ne
  • Title Language Code
    eng
  • Text Language Code
    eng
  • Place of Publication
    Dordrecht ; Boston
  • Pages/Volumes
    xi, 381 p.
  • Size
    25 cm
  • Classification
  • Subject Headings
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