Power Algebras over Semirings: With Applications in Mathematics and Computer Science / Edition 1

Power Algebras over Semirings: With Applications in Mathematics and Computer Science / Edition 1

by Jonathan S. Golan
     
 

ISBN-10: 9048152704

ISBN-13: 9789048152704

Pub. Date: 12/08/2010

Publisher: Springer Netherlands

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

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Overview

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 Höhle 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.

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Product Details

ISBN-13:
9789048152704
Publisher:
Springer Netherlands
Publication date:
12/08/2010
Series:
Mathematics and Its Applications (closed) Series, #488
Edition description:
Softcover reprint of hardcover 1st ed. 1999
Pages:
206
Product dimensions:
6.10(w) x 9.25(h) x 0.02(d)

Related Subjects

Table of Contents

Preface. Some (hopefully) motivating examples. 0. Background material. 1. Powers of a semiring. 2. Relations with values in a semiring. 3. Change of base semirings. 4. Convolutions. 5. Semiring-valued subsemigroups and submonoids. 6. Semiring-valued groups. 7. Semiring-valued submodules and subspaces. 8. Semiring-ideals in semirings and rings. References. Index.

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