Mathematics and Its Applications

With Applications in Mathematics and Computer Science

By: Jonathan S. Golan

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Hardcover | 31 July 1999

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220 Pages

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24.77 x 16.51 x 1.91

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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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You Can Find This Book In

Non-Fiction Mathematics Algebra Medicine Medicine in General Groups & Group Theory Mathematical Foundation Mathematical Logic Computing & I.T.Databases Data Capture & Analysis Computer Science

Preface
Some (hopefully) motivating examples	p. 1
Background material	p. 7
Powers of a semiring	p. 27
Relations with values in a semiring	p. 37
Change of base semirings	p. 61
Convolutions	p. 67
Semiring-valued subsemigroups and submonoids	p. 89
Semiring-valued groups	p. 113
Semiring-valued submodules and subspaces	p. 141
Semiring-valued ideals in semirings and rings	p. 155
References	p. 169
Index	p. 189
Table of Contents provided by Blackwell. All Rights Reserved.

Mathematics and Its Applications

With Applications in Mathematics and Computer Science

At a Glance

Hardcover

Shipping

How to return your order

Defective items

You Can Find This Book In

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