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Archiv der Mathematik

, Volume 106, Issue 4, pp 323–325 | Cite as

A counterexample for lightning flash modules over E(e 1, e 2)

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Abstract

We give a counterexample to Theorem 5 in Section 18.2 of Margolis’ book, “Spectra and the Steenrod Algebra” and make remarks about the proofs of some later theorems in the book that depend on it. The counterexample is a module which does not split as a sum of lightning flash modules and free modules.

Keywords

Steenrod algebra Lightning flash Graded exterior algebra 

Mathematics Subject Classification

55S10 16W50 
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References

  1. 1.
    Adams J.F., Margolis H.R.: Modules over the Steenrod algebra. Topology 10, 271–282 (1971)MathSciNetCrossRefMATHGoogle Scholar
  2. 2.
    H. R. Margolis, Spectra and the Steenrod algebra, North Holland, Amsterdam, 1983.Google Scholar
  3. 3.
    Ringel C.M.: The indecomposable representations of the dihedral 2-groups. Math. Ann. 214, 19–34 (1975)MathSciNetCrossRefMATHGoogle Scholar

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© The Author(s) 2016

Open AccessThis article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.

Authors and Affiliations

  1. 1.University of AberdeenAberdeenUK
  2. 2.Department of MathematicsWayne State UniversityDetroitUSA

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