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Power Algebras Over Semirings

Jonathan S. Golan

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ISBN 10: 9048152704 / ISBN 13: 9789048152704
Published by Springer
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Paperback. 206 pages. Dimensions: 9.2in. x 6.1in. x 0.5in.This monograph is a continuation of several themes presented in my previous books 146, 149. In those volumes, I was concerned primarily with the properties of semirings. Here, the objects of investigation are sets of the form RA, where R is a semiring and A is a set having a certain structure. The problem is one of translating that structure to RA in some natural way. As such, it tries to find a unified way of dealing with diverse topics in mathematics and theoretical com puter science as formal language theory, the theory of fuzzy algebraic structures, models of optimal control, and many others. Another special case is the creation of idempotent analysis and similar work in optimization theory. Unlike the case of the previous work, which rested on a fairly established mathematical foundation, the approach here is much more tentative and docimastic. This is an introduction to, not a definitative presentation of, an area of mathematics still very much in the making. The basic philosphical problem lurking in the background is one stated suc cinctly by Hahle and Sostak 185: . . . to what extent basic fields of mathematics like algebra and topology are dependent on the underlying set theory The conflicting definitions proposed by various researchers in search of a resolution to this conundrum show just how difficult this problem is to see in a proper light. This item ships from multiple locations. Your book may arrive from Roseburg,OR, La Vergne,TN. Bookseller Inventory # 9789048152704

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Bibliographic Details

Title: Power Algebras Over Semirings

Publisher: Springer

Binding: Paperback

Book Condition:New

Book Type: Paperback

About this title

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This monograph is a continuation of several themes presented in my previous books [146, 149]. In those volumes, I was concerned primarily with the properties of semirings. Here, the objects of investigation are sets of the form RA, where R is a semiring and A is a set having a certain structure. The problem is one of translating that structure to RA in some "natural" way. As such, it tries to find a unified way of dealing with diverse topics in mathematics and theoretical com­ puter science as formal language theory, the theory of fuzzy algebraic structures, models of optimal control, and many others. Another special case is the creation of "idempotent analysis" and similar work in optimization theory. Unlike the case of the previous work, which rested on a fairly established mathematical foundation, the approach here is much more tentative and docimastic. This is an introduction to, not a definitative presentation of, an area of mathematics still very much in the making. The basic philosphical problem lurking in the background is one stated suc­ cinctly by Hahle and Sostak [185]: ". . . to what extent basic fields of mathematics like algebra and topology are dependent on the underlying set theory?" The conflicting definitions proposed by various researchers in search of a resolution to this conundrum show just how difficult this problem is to see in a proper light.

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