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Power Algebras over Semirings - With Applications in Mathematics and Computer Science (Paperback, Softcover reprint of hardcover 1st ed. 1999)
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Power Algebras over Semirings - With Applications in Mathematics and Computer Science (Paperback, Softcover reprint of hardcover 1st ed. 1999)
Series: Mathematics and Its Applications, 488
Expected to ship within 10 - 15 working days
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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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