Download e-book for iPad: A Guide to the Literature on Semirings and their by Kazimierz Głazek (auth.)

By Kazimierz Głazek (auth.)

ISBN-10: 904816060X

ISBN-13: 9789048160600

ISBN-10: 9401599645

ISBN-13: 9789401599641

This quantity offers a quick advisor to the broad literature touching on semir­ ings in addition to a whole bibliography. The literature has been created over decades, in number of languages, through authors representing assorted faculties of arithmetic and dealing in a number of comparable fields. routinely the terminology used isn't really common, which additional compounds the trouble of finding pertinent resources even during this age of the net and digital dis­ semination of analysis effects. thus far there was no unmarried reference which can consultant the student or scholar to the proper guides. This ebook is an try to fill this hole. My curiosity within the idea of semirings begun within the early sixties, while to­ gether with Bogdan W ~glorz i attempted to enquire a few algebraic facets of compactifications of topological areas, semirings of semicontinuous services, and the final perfect idea for detailed semirings. (Unfortunately, neighborhood alge­ braists in Poland informed me at the moment that there has been not anything fascinating in investigating semiring conception simply because ring thought used to be nonetheless being developed). even if, your time later we turned conscious of a few comparable investigations hav­ ing already been performed. the idea of semirings has remained "my past love" ever given that, and i've been drawn to the implications during this box which have been showing in literature (even although i have never been energetic during this sector myself).

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R. H. , the following papers: L. R. A. R. Johnson & L. Elsner [1987]) lead to many examples of semirings. , by J. Horst [1969], B. J. Wisner [1966], G. Z. Kwiatkowska, G. A. Parker & R. N. Pandit [1961]' G. M. H. S. H. Teh [1966]. G. Horne, Jr. P. -S. P. -S. Tam [1997]). Some aspects of this semi ring are related to the concept of Baer semiring and Baer *-semiring introduced recently by Barker and Tam. One can also consider matrices over semirings. Certain machine-scheduling problems can be reduced to finding eigenvectors and eigenvalues of matrices over some semirings.

S. ', see: M. E. Rutherford [1963b], H. Straubing [1983], M. Gondran [1983], P. J. Olsder & C. -M. L. Baccelli, G. J. -P. S. Golan [1992J (p. 199-200), [1999aJ; for some generalization of Cramer's rule for the max-plus algebra, called also the max or schedule algebr'a, (IE. J. Olsder & C. Roos [1988J. -H. W. -H. W. B. B. Wagoner [1990], and also M. Boyle & D. Handelman [1993]). Such an equivalence over N U{O} has important applications to topological dynamics and the study of diffeomorphisms. G.

S. J. G. J. -Z. Song [1994a], A. B. Kim [1984]' K-H. Kim [1979], K-H. W. Roush [1977], [1979a], [1981a], [1981c], [1981d]' [1986]' [1992], KH. W. Roush & G. -H. W. Roush & W. Schonfeld [1977], S. J. Pullman [1992]' D. Krob [1990], S. D. G. E. Rutherford [1963a], [1964a], [1964b], S. A. -Z. -Z. -G. Lee [1995], S. Warshall [1962]' Linear Algebra over Semirings 39 and M. Yoeli [1961]. It is worth adding that results of S. Warshall on Boolean matrices provide a theoretical foundation for some algorithms; see R Floyd [1962]' for instance.

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A Guide to the Literature on Semirings and their Applications in Mathematics and Information Sciences: With Complete Bibliography by Kazimierz Głazek (auth.)

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