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

David Benson; Robert R. Bruner

doi:10.1007/s00013-016-0880-8

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

David Benson, Robert R. Bruner

Mathematical Science

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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.

Original language	English
Pages (from-to)	323-325
Number of pages	3
Journal	Archiv der Mathematik
Volume	106
Issue number	4
Early online date	23 Feb 2016
DOIs	https://doi.org/10.1007/s00013-016-0880-8
Publication status	Published - Apr 2016

Keywords

steenrod algebra
lightning flash
graded exterior algebra

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10.1007/s00013-016-0880-8Licence: CC BY

A counterexample for lightning flash modules over E(e 1, e 2)
This 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.
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Cite this

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

abstract = "We give a counterexample to Theorem 5 in Section 18.2 of Margolis{\textquoteright} 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",

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note = "This work was partially supported by the Simons Foundation and by the Mathematisches Forschungsinstitut Oberwolfach.",

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AU - Bruner, Robert R.

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N2 - 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.

AB - 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.

KW - steenrod algebra

KW - lightning flash

KW - graded exterior algebra

U2 - 10.1007/s00013-016-0880-8

DO - 10.1007/s00013-016-0880-8

M3 - Article

VL - 106

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EP - 325

JO - Archiv der Mathematik

JF - Archiv der Mathematik

SN - 0003-889X

IS - 4

ER -

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

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Keywords

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