Power Algebras over Semirings
Subtitle: With Applications in Mathematics and Computer Science
By: by Jonathan S. Golan
Series: Mathematics and Its Applications -- 488; Mathematics and Its Applications -- 488
Publisher: Springer Netherlands
Published: 1999
Place of publication: Dordrecht
Language: eng
Format: [electronic resource] :
Number of pages: 206
ISBN-13: 9789048152704; 9789401592413
Subjects: Mathematics; Computational complexity; Symbolic and mathematical Logic; Algebra
Description: 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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