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Sonata: a GAP tool for nearring computations

Published:04 November 2016Publication History
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Abstract

A nearring N is an algebra that does not satisfy the ring axioms, but nevertheless satisfies a one-sided distributivity law. SONATA is a GAP package designed as a research tool for nearrings. Users are able to define and work with finite nearrings in order to generate and test conjectures.

References

  1. E. Aichinger. Generating polynomials using function composition. Quaest. Math., 36(1):39--46, 2013.Google ScholarGoogle ScholarCross RefCross Ref
  2. E. Aichinger, F. Binder, J. Ecker, P. Mayr, and C. Nöbauer. SONATA - system of near-rings and their applications, GAP package, Version 2.8, 2015. (http://www.algebra.uni-linz.ac.at/Sonata/).Google ScholarGoogle Scholar
  3. J. R. Clay. Nearrings: Geneses and Applications. Oxford University Press - Oxford, New York, Tokyo, 1992.Google ScholarGoogle Scholar
  4. G. Ferrero. Stems planari e BIB-disegni. Riv. Mat. Uni. Parma, 11(2):79--96, 1970.Google ScholarGoogle Scholar
  5. The GAP Group. GAP - Groups, Algorithms, and Programming, Version 4.8.3, 2016.Google ScholarGoogle Scholar
  6. Peter Mayr. The polynomial functions on Frobenius complements. Acta Sci. Math. (Szeged), 72(1--2):37--50, 2006.Google ScholarGoogle Scholar
  7. J. D. P. Meldrum. Near-rings and their links with groups. Pitman (Advanced Publishing Program), Boston, Mass., 1985.Google ScholarGoogle Scholar
  8. G. F. Pilz. Near-rings. North-Holland Publishing Company - Amsterdam, New York, Oxford, 2nd edition, 1983.Google ScholarGoogle Scholar
  9. H. Zassenhaus. über endliche Fastköper. Abh. Math. Semin. Univ. Hamb., 11:187--220, 1935.Google ScholarGoogle ScholarCross RefCross Ref

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  • Published in

    cover image ACM Communications in Computer Algebra
    ACM Communications in Computer Algebra  Volume 50, Issue 3
    September 2016
    46 pages
    ISSN:1932-2240
    DOI:10.1145/3015306
    Issue’s Table of Contents

    Copyright © 2016 Authors

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    Association for Computing Machinery

    New York, NY, United States

    Publication History

    • Published: 4 November 2016

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