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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Eilenberg-Mac Lane spectra


Author: H. R. Margolis
Journal: Proc. Amer. Math. Soc. 43 (1974), 409-415
MSC: Primary 55G10
MathSciNet review: 0341488
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Abstract: Let $ K({Z_p})$ be the Eilenberg-Mac Lane spectrum with homotopy $ {Z_p}$ and let $ A = {H^ \ast }(K({Z_p});{Z_p})$--the $ \bmod p$ Steenrod algebra. Let $ X$ be a locally finite spectrum. It is proven that

$\displaystyle [K({Z_p}),X] \to {\operatorname{Hom} _A}({H^ \ast }(X;{Z_p}),A)$

is an isomorphism. It is also proven that there is a unique decomposition $ X = ( \oplus K({Z_p})) \oplus Y$ where $ {H^ \ast }(Y;{Z_p})$ as an $ A$-module has no free summands.

References [Enhancements On Off] (What's this?)

  • [1] J. F. Adams and H. R. Margolis, Modules over the Steenrod algebra, Topology 10 (1971), 271–282. MR 0294450 (45 #3520)
  • [2] J. M. Boardman, Stable homotopy theory, Warwick lecture notes series (1965).
  • [3] -, Stable homotopy theory, Chap. II, preprint (1970).
  • [4] H. R. Margolis, Modules over the Steenrod algebra and stable homotopy theory, (to appear).
  • [5] John C. Moore and Franklin P. Peterson, Nearly Frobenius algebras, Poincaré algebras and their modules, J. Pure Appl. Algebra 3 (1973), 83–93. MR 0335572 (49 #353)
  • [6] R. M. Vogt, Boardman's stable homotopy category, Lecture Note Series, no. 21, Aarhus Univ., Aarhus, 1970. MR 43 #1187.

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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1974-0341488-9
PII: S 0002-9939(1974)0341488-9
Keywords: Eilenberg-Mac Lane spectra, Steenrod algebra
Article copyright: © Copyright 1974 American Mathematical Society