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Multiplication Modules and a Theorem of P. F. Smith

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Abstract

P. F. Smith [7, Theorem 8] gave sufficient conditions on a finite set of modules for their sum and intersection to be multiplication modules. We give sufficient conditions on an arbitrary set of multiplication modules for the intersection to be a multiplication module. We generalize Smith"s theorem, and we prove conditions on sums and intersections of sets of modules sufficient for them to be multiplication modules.

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Authors and Affiliations

  1. Department of Mathematics, University of Auckland, Auckland, New Zealand

    Majid M. Ali & David J. Smith

Authors
  1. Majid M. Ali
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  2. David J. Smith
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Ali, M.M., Smith, D.J. Multiplication Modules and a Theorem of P. F. Smith. Periodica Mathematica Hungarica 44, 127–135 (2002). https://doi.org/10.1023/A:1019680010738

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  • DOI: https://doi.org/10.1023/A:1019680010738

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