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Table of contents (12 chapters)
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Front Matter
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Back Matter
Keywords
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.
Reviews
From the reviews:
"The author points out that many important applications of semiring theory can be reduced to the problem of finding solutions of affine equations … . theory with complete proofs as well as illustrating examples can be found. A carefully written index of applications and an index of terminology help the reader to find the numerous concepts mentioned throughout the book. Also an extensive bibliography (490 titles) is included to show the wide range of applications of the developed concepts in many areas … ." (Udo Hebisch, Zentralblatt MATH, Vol. 1042, 2004)
Authors and Affiliations
Bibliographic Information
Book Title: Semirings and Affine Equations over Them
Book Subtitle: Theory and Applications
Authors: Jonathan S. Golan
Series Title: Mathematics and Its Applications
DOI: https://doi.org/10.1007/978-94-017-0383-3
Publisher: Springer Dordrecht
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eBook Packages: Springer Book Archive
Copyright Information: Springer Science+Business Media Dordrecht 2003
Hardcover ISBN: 978-1-4020-1358-4Published: 30 June 2003
Softcover ISBN: 978-90-481-6310-6Published: 10 April 2011
eBook ISBN: 978-94-017-0383-3Published: 14 March 2013
Edition Number: 1
Number of Pages: XIII, 241
Topics: Associative Rings and Algebras, Discrete Mathematics in Computer Science, Mathematical Modeling and Industrial Mathematics, Calculus of Variations and Optimal Control; Optimization, Mathematical Logic and Foundations