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Symbolic Rewriting Techniques pp 277–288Cite as

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Deciding Degree-Four-Identities for Alternative Rings by Rewriting

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Part of the book series: Progress in Computer Science and Applied Logic ((PCS,volume 15))

Abstract

Rewriting can be used to prove automatically identities for alternative rings, see for example [7], but no complete rewrite system is known. In this paper I give rewrite systems for several classes of alternative rings which can be used to decide whether an equation up to degree 4 is an identity for the class of rings considered. For the class of strongly left alternative rings I was able to compute an analogous rewrite system for degree 5.

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References

  1. Beck, R.E.; Kolman, B. (eds): Computers in Nonassociative Rings and Algebras, Academic Press, New York 1977.

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  5. Kleinfeld, E.; Humm, M.: A nonidentity for right alternative rings. Proc. Amer. Math. Soc. 22 (1969), 109–110.

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  6. Widiger, A.: Termersetzungssysteme zum Beweis von Identitäten bis zum Grad 4 in Klassen alternativer Ringe. Rostocker Informatik-Berichte 16 (1994), 77–99.

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  7. Zhang, H.: A case study of completion modulo distributivity and abelian groups. In Kirchner, C. (ed.): Rewriting Techniques and Applications, Lecture Notes in Computer Science 690, 32–46, Springer-Verlag, Berlin 1993.

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Author information

Authors and Affiliations

  1. Fachbereich Informatik, Universität Rostock, D-18051, Rostock, Germany

    Alfred Widiger

Authors
  1. Alfred Widiger
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Editor information

Editors and Affiliations

  1. INRIA, 2004, Route des lucioles, BP 93, 06902, Sophia Antipolis Cedex, France

    Manuel Bronstein

  2. FMI Universität Passau, 94030, Passau, Germany

    Volker Weispfenning

  3. IBM Deutschland Informationssysteme GmbH, Postfach 10 30 68, 69020, Heidelberg, Germany

    Johannes Grabmeier

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© 1998 Springer Basel AG

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Widiger, A. (1998). Deciding Degree-Four-Identities for Alternative Rings by Rewriting. In: Bronstein, M., Weispfenning, V., Grabmeier, J. (eds) Symbolic Rewriting Techniques. Progress in Computer Science and Applied Logic, vol 15. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-8800-4_14

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  • DOI: https://doi.org/10.1007/978-3-0348-8800-4_14

  • Publisher Name: Birkhäuser, Basel

  • Print ISBN: 978-3-0348-9779-2

  • Online ISBN: 978-3-0348-8800-4

  • eBook Packages: Springer Book Archive

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