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Author: Hanns Joachim Weinert
Publisher: World Scientific
ISBN: 9814495697
Category : Mathematics
Languages : en
Pages : 371
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Book Description
This book provides an introduction to the algebraic theory of semirings and, in this context, to basic algebraic concepts as e.g. semigroups, lattices and rings. It includes an algebraic theory of infinite sums as well as a detailed treatment of several applications in theoretical computer science. Complete proofs, various examples and exercises (some of them with solutions) make the book suitable for self-study. On the other hand, a more experienced reader who looks for information about the most common concepts and results on semirings will find cross-references throughout the book, a comprehensive bibliography and various hints to it.
Author: Hanns Joachim Weinert
Publisher: World Scientific
ISBN: 9814495697
Category : Mathematics
Languages : en
Pages : 371
Get Book Here
Book Description
This book provides an introduction to the algebraic theory of semirings and, in this context, to basic algebraic concepts as e.g. semigroups, lattices and rings. It includes an algebraic theory of infinite sums as well as a detailed treatment of several applications in theoretical computer science. Complete proofs, various examples and exercises (some of them with solutions) make the book suitable for self-study. On the other hand, a more experienced reader who looks for information about the most common concepts and results on semirings will find cross-references throughout the book, a comprehensive bibliography and various hints to it.
Author: Jonathan S. Golan
Publisher: Springer Science & Business Media
ISBN: 9401592411
Category : Mathematics
Languages : en
Pages : 207
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Book Description
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.
Author: K. Glazek
Publisher: Springer Science & Business Media
ISBN: 9401599645
Category : Mathematics
Languages : en
Pages : 394
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Book Description
This volume presents a short guide to the extensive literature concerning semir ings along with a complete bibliography. The literature has been created over many years, in variety of languages, by authors representing different schools of mathematics and working in various related fields. In many instances the terminology used is not universal, which further compounds the difficulty of locating pertinent sources even in this age of the Internet and electronic dis semination of research results. So far there has been no single reference that could guide the interested scholar or student to the relevant publications. This book is an attempt to fill this gap. My interest in the theory of semirings began in the early sixties, when to gether with Bogdan W ~glorz I tried to investigate some algebraic aspects of compactifications of topological spaces, semirings of semicontinuous functions, and the general ideal theory for special semirings. (Unfortunately, local alge braists in Poland told me at that time that there was nothing interesting in investigating semiring theory because ring theory was still being developed). However, some time later we became aware of some similar investigations hav ing already been done. The theory of semirings has remained "my first love" ever since, and I have been interested in the results in this field that have been appearing in literature (even though I have not been active in this area myself).
Author: Jonathan S. Golan
Publisher: Springer Science & Business Media
ISBN: 9401593337
Category : Mathematics
Languages : en
Pages : 376
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Book Description
There is no branch of mathematics, however abstract, which may not some day be applied to phenomena of the real world. - Nikolai Ivanovich Lobatchevsky This book is an extensively-revised and expanded version of "The Theory of Semirings, with Applicationsin Mathematics and Theoretical Computer Science" [Golan, 1992], first published by Longman. When that book went out of print, it became clear - in light of the significant advances in semiring theory over the past years and its new important applications in such areas as idempotent analysis and the theory of discrete-event dynamical systems - that a second edition incorporating minor changes would not be sufficient and that a major revision of the book was in order. Therefore, though the structure of the first «dition was preserved, the text was extensively rewritten and substantially expanded. In particular, references to many interesting and applications of semiring theory, developed in the past few years, had to be added. Unfortunately, I find that it is best not to go into these applications in detail, for that would entail long digressions into various domains of pure and applied mathematics which would only detract from the unity of the volume and increase its length considerably. However, I have tried to provide an extensive collection of examples to arouse the reader's interest in applications, as well as sufficient citations to allow the interested reader to locate them. For the reader's convenience, an index to these citations is given at the end of the book .
Author: Michel Gondran
Publisher: Springer Science & Business Media
ISBN: 0387754504
Category : Business & Economics
Languages : en
Pages : 401
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Book Description
The primary objective of this essential text is to emphasize the deep relations existing between the semiring and dioïd structures with graphs and their combinatorial properties. It does so at the same time as demonstrating the modeling and problem-solving flexibility of these structures. In addition the book provides an extensive overview of the mathematical properties employed by "nonclassical" algebraic structures which either extend usual algebra or form a new branch of it.
Author: Jonathan S. Golan
Publisher: Springer Science & Business Media
ISBN: 9401703833
Category : Mathematics
Languages : en
Pages : 243
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Book Description
Semiring theory stands with a foot in each of two mathematical domains. The first being abstract algebra and the other the fields of applied mathematics such as optimization theory, the theory of discrete-event dynamical systems, automata theory, and formal language theory, as well as from the allied areas of theoretical computer science and theoretical physics. Most important applications of semiring theory in these areas turn out to revolve around the problem of finding the equalizer of a pair of affine maps between two semimodules. In this volume, we chart the state of the art on solving this problem, and present many specific cases of applications. This book is essentially the third part of a trilogy, along with Semirings and their Applications, and Power Algebras over Semirings, both written by the same author and published by Kluwer Academic Publishers in 1999. While each book can be read independently of the others, to get the full force of the theory and applications one should have access to all three. This work will be of interest to academic and industrial researchers and graduate students. The intent of the book is to bring the applications to the attention of the abstract mathematicians and to make the abstract mathematics available to those who are using these tools in an ad-hoc manner without realizing the full force of the theory.
Author: Lars Garding
Publisher: Springer Science & Business Media
ISBN: 1461387973
Category : Mathematics
Languages : en
Pages : 206
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Book Description
The aim of this book is to teach the reader the topics in algebra which are useful in the study of computer science. In a clear, concise style, the author present the basic algebraic structures, and their applications to such topics as the finite Fourier transform, coding, complexity, and automata theory. The book can also be read profitably as a course in applied algebra for mathematics students.
Author: Jonathan S. Golan
Publisher:
ISBN:
Category : Rings (Algebra)
Languages : en
Pages : 342
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Book Description
Author: Polly Wee Sy
Publisher: World Scientific
ISBN: 9814366315
Category : Mathematics
Languages : en
Pages : 755
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Book Description
This volume is an outcome of the International Conference on Algebra in celebration of the 70th birthday of Professor Shum Kar-Ping which was held in Gadjah Mada University on 7OCo10 October 2010. As a consequence of the wide coverage of his research interest and work, it presents 54 research papers, all original and referred, describing the latest research and development, and addressing a variety of issues and methods in semigroups, groups, rings and modules, lattices and Hopf Algebra. The book also provides five well-written expository survey articles which feature the structure of finite groups by A Ballester-Bolinches, R Esteban-Romero, and Yangming Li; new results of GrAbner-Shirshov basis by L A Bokut, Yuqun Chen, and K P Shum; polygroups and their properties by B Davvaz; main results on abstract characterizations of algebras of n-place functions obtained in the last 40 years by Wieslaw A Dudek and Valentin S Trokhimenko; Inverse semigroups and their generalizations by X M Ren and K P Shum. Recent work on cones of metrics and combinatorics done by M M Deza et al. is included."
Author: Mariana Durcheva
Publisher: Cambridge Scholars Publishing
ISBN: 1527543315
Category : Mathematics
Languages : en
Pages : 132
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Book Description
Semirings as an algebraic structure have been known since 1934, but remained unapplied for mathematical purposes for a long time. It has only been in the past decade that they have been used in cryptography. The advantage of (additively) idempotent semirings is that the additive operation does not have an inverse, which can help in preventing the breakage of a cryptosystem. This book describes a number of cryptographic protocols, as well as the hard mathematical problems on which their security is based. It will appeal to cryptographers and specialists in applied algebra.
