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The Algebraic Theory of Semirings

In: A Guide to the Literature on Semirings and their Applications in Mathematics and Information Sciences

Author

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  • Kazimierz Głazek

    (University of Zielona Góra, Institute of Mathematics)

Abstract

Intensive investigations of the algebraic theory of semirings were started in the 1950s mostly by A. Almeida-Costa (in Portugal), S. Bourne, M. Henriksen and H. Zassenhaus (in the USA), L. Rédei and O. Steinfeld (in Hungary), K. Iséki and K. Iizuka (in Japan) , H.J. Weinert and H. Lugowski (in Germany) , W. Słowikowski and W. Zawadowski (in Poland), and by their co-workers. Several classical notions and theorems from the theory of rings were extended and generalized to semirings. The semiring ℕ of natural numbers was the first interesting model for such investigations which is not a ring. Many papers were devoted to the theory of ideals, congruences, radicals and lattices of ideals of semirings. The first introduction to the theory of ideals of semirings was given by A. Almeida Costa [1974]. As the monographs by J.S. Golan [1992], [1999a], and by U. Hebisch & H.J. Weinert [1993] and [1998] provide an excellent introduction to that theory, we will only list papers relating to that area, omitting additional details.

Suggested Citation

  • Kazimierz Głazek, 2002. "The Algebraic Theory of Semirings," Springer Books, in: A Guide to the Literature on Semirings and their Applications in Mathematics and Information Sciences, chapter 2, pages 11-23, Springer.
    • Handle: RePEc:spr:sprchp:978-94-015-9964-1_3
    DOI: 10.1007/978-94-015-9964-1_3
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