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.
Algebraic Geometry | Geometry and Topology
Benson, D. & Bruner, R. A counterexample for lightning flash modules over E(e1,e2). Arch. Math. 106, 323–325 (2016). https://doi.org/10.1007/s00013-016-0880-8