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.
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Adams J.F., Margolis H.R.: Modules over the Steenrod algebra. Topology 10, 271–282 (1971)
H. R. Margolis, Spectra and the Steenrod algebra, North Holland, Amsterdam, 1983.
Ringel C.M.: The indecomposable representations of the dihedral 2-groups. Math. Ann. 214, 19–34 (1975)
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This work was partially supported by the Simons Foundation and by the Mathematisches Forschungsinstitut Oberwolfach.
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Benson, D., Bruner, R.R. A counterexample for lightning flash modules over E(e 1, e 2). Arch. Math. 106, 323–325 (2016). https://doi.org/10.1007/s00013-016-0880-8
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DOI: https://doi.org/10.1007/s00013-016-0880-8