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Semirings and their Applications - Jonathan S. Golan

Semirings and their Applications

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Published: 31st July 1999
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This work is an updated and considerably expanded version of the author's book The Theory of Semirings, with Applications to Mathematics and Theoretical Science, which has been recognized as the definitive reference work in this area. This edition includes many of the new results in this area, as well as further applications of semiring theory in such areas as idempotent analysis, discrete dynamical systems, formal language theory, fuzzy set theory, optimization etc. The book contains an extensive bibliography and a large number of examples.

Audience: This book is aimed both at mathematicians and at researchers in applied mathematics and theoretical computer science. It is also suitable for use as a graduate-level textbook.

Preface
Hemirings and semirings: definitions and examplesp. 1
Sets and relations with values in a semiringp. 19
Building new semirings from oldp. 27
Some conditions on semiringsp. 43
Complemented elements in semiringsp. 59
Ideals in semiringsp. 65
Prime and semiprime ideals in semiringsp. 85
Factor semiringsp. 95
Morphisms of semiringsp. 105
Kernels of morphismsp. 121
Semirings of fractionsp. 129
Euclidean semiringsp. 135
Additively-regular semiringsp. 143
Semimodules over semiringsp. 149
Factor semimodulesp. 163
Some constructions for semimodulesp. 181
Free, projective, and injective semimodulesp. 191
Localization of semimodulesp. 203
Linear algebra over a semiringp. 211
Partially-ordered semiringsp. 223
Lattice-ordered semiringsp. 239
Complete semiringsp. 247
Complete semimodulesp. 259
CLO-semiringsp. 267
Fixed points of affine mapsp. 285
Referencesp. 307
Index of applicationsp. 355
Index of terminologyp. 357
Table of Contents provided by Blackwell. All Rights Reserved.

ISBN: 9780792357865
ISBN-10: 0792357868
Audience: Professional
Format: Hardcover
Language: English
Number Of Pages: 382
Published: 31st July 1999
Publisher: Springer
Country of Publication: NL
Dimensions (cm): 24.13 x 16.51  x 2.54
Weight (kg): 0.74