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Power Algebras over Semirings : With Applications in Mathematics and Computer Science - Jonathan S. Golan

Power Algebras over Semirings

With Applications in Mathematics and Computer Science

Hardcover Published: 31st July 1999
ISBN: 9780792358343
Number Of Pages: 206

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This research monograph investigates sets of the form RA where R is a semiring, and A is a set with a certain structure. Such constructs generalise fuzzy and toll algebraic structures, which in recent years have shown themselves of importance in engineering and computer science, as well as in new mathematical disciplines like idempotent analysis. This volume puts much of the ad hoc work of the past decade on a firm mathematical foundation by creating a unified approach which has important implications in such diverse areas as formal language theory, discrete dynamical systems, models of optimal control, and many others.

This book also seeks to address the fundamental question posed by HAhle and Sostak as to what extent basic fields of mathematics like algebra and topology are dependent on the underlying set theory.

Since the development of a new mathematical theory is basically inductive, this book begins with a large number of instances which appear in various mathematical contexts, and then develops a general abstract framework, with many examples which will encourage further study in greater depth.

Audience: This work will be of interest to mathematicians whose work involves associative rings and algebras, ordered algebraic structures, optimal control, graph theory, fuzzy sets and fuzzy algebraic structures.

Preface
Some (hopefully) motivating examplesp. 1
Background materialp. 7
Powers of a semiringp. 27
Relations with values in a semiringp. 37
Change of base semiringsp. 61
Convolutionsp. 67
Semiring-valued subsemigroups and submonoidsp. 89
Semiring-valued groupsp. 113
Semiring-valued submodules and subspacesp. 141
Semiring-valued ideals in semirings and ringsp. 155
Referencesp. 169
Indexp. 189
Table of Contents provided by Blackwell. All Rights Reserved.

ISBN: 9780792358343
ISBN-10: 0792358341
Series: MATHEMATICS AND ITS APPLICATIONS (KLUWER )
Audience: Professional
Format: Hardcover
Language: English
Number Of Pages: 206
Published: 31st July 1999
Publisher: Springer
Country of Publication: NL
Dimensions (cm): 24.77 x 16.51  x 1.91
Weight (kg): 0.49

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