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Automated Deduction in Ring Theory

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Mathematical Software – ICMS 2016 (ICMS 2016)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 9725))

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Abstract

Pover9/Mace4 or its predecessor Otter is one of the powerful automated theorem provers for first-order and equational logic. In this paper we explore various possibilities of using Prover9 in ring theory and semiring theory, in particular, associative rings, rings with involutions, semirings with cancellation laws and near-rings. We code the corresponding axioms in Prover9, check some well-known theorems, for example, Jacobson’s commutativity theorem, give some new proofs, and also present some new results.

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Acknowledgements

This research was partially supported by the grants from the Natural Sciences and Engineering Research Council of Canada (NSERC).

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Authors and Affiliations

  1. Department of Mathematics, University of Manitoba, Winnipeg, R3T 2N2, Canada

    Ranganathan Padmanabhan & Yang Zhang

Authors
  1. Ranganathan Padmanabhan
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  2. Yang Zhang
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Corresponding author

Correspondence to Yang Zhang .

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Editors and Affiliations

  1. Universität Kaiserslautern , Kaiserslautern, Germany

    Gert-Martin Greuel

  2. Zuse Institute Berlin , Berlin, Germany

    Thorsten Koch

  3. Johannes Kepler University Linz , Hagenberg, Austria

    Peter Paule

  4. University of Notre Dame , Notre Dame, Indiana, USA

    Andrew Sommese

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Padmanabhan, R., Zhang, Y. (2016). Automated Deduction in Ring Theory. In: Greuel, GM., Koch, T., Paule, P., Sommese, A. (eds) Mathematical Software – ICMS 2016. ICMS 2016. Lecture Notes in Computer Science(), vol 9725. Springer, Cham. https://doi.org/10.1007/978-3-319-42432-3_9

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  • DOI: https://doi.org/10.1007/978-3-319-42432-3_9

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-42431-6

  • Online ISBN: 978-3-319-42432-3

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