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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 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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Previews available in: English
Showing 2 featured editions. View all 2 editions?
Edition | Availability |
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1
Power Algebras over Semirings: With Applications in Mathematics and Computer Science
Jan 07, 2013, Springer
paperback
940159242X 9789401592420
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2
Power Algebras over Semirings: With Applications in Mathematics and Computer Science
1999, Springer Netherlands
electronic resource :
in English
9048152704 9789048152704
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- Created July 6, 2019
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March 1, 2022 | Edited by ImportBot | import existing book |
December 29, 2021 | Edited by ImportBot | import existing book |
July 6, 2019 | Created by MARC Bot | Imported from Internet Archive item record. |