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Commutative 2-local ring spectra

Published online by Cambridge University Press:  14 November 2011

L. Astey
L. Astey
Affiliation:
Department of Mathematics, Centro de Investigacion del IPN, Apartado 14-740, Mexico, DF 07000, Mexico
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Abstract

A theorem is proved characterising representable, multiplicative commutative cohomology theories that split as sums of singular cohomologies after localisation at 2. This theorem is shown to be equivalent to one proved by Würgler and Pazhitnov and Rudyak, for which we provide a simplified proof. We also provide a simple proof of a related theorem of Boardman.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 127 , Issue 1 , 1997 , pp. 1 - 10
Copyright
Copyright © Royal Society of Edinburgh 1997

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References

1Adams, J. F.. Stable Homotopy and Generalized Homology (Chicago: University of Chicago Press, 1974).Google Scholar
2Araki, S. and Toda, H.. Multiplicative structures in mod q cohomology theories II. Osaka J. Math. 3 (1966), 81–120.Google Scholar
3Baas, N. A. and Madsen, I.. On the realization of certain modules over the Steenrod algebra. Math. Scand. 31(1972), 220–4.CrossRefGoogle Scholar
4Boardman, J. M.. Graded Eilenberg-MacLane ring spectra. Amer. J. Math. 102 (1980), 979–1010.CrossRefGoogle Scholar
5Milnor, J. W.. The Steenrod algebra and its dual. Ann. Math. 67 (1958), 150–71.CrossRefGoogle Scholar
6Mironov, O. K.. Multiplications in cobordism theories with singularities and Steenrod-tom Dieck operations. Math. USSR Izv. 13 (1979), 89–106.CrossRefGoogle Scholar
7Pazhitnov, A. V. and Rudyak, Yu. B.. On commutative ring spectra of characteristic 2. Math. USSR Sb. 52(1985), 471–9.CrossRefGoogle Scholar
8Ravenel, D. C. and Wilson, W. S.. The Hopf ring for complex cobordism. J. Pure Appl. Algebra 9 (1977), 241–80.CrossRefGoogle Scholar
9Wall, C. T. C.. Determination of the cobordism ring. Ann. Math. 72 (1960), 292–311.CrossRefGoogle Scholar
10Würgler, U.. On products in a family of cohomology theories associated to the invariant prime ideals of π*;BP. Comment. Math. Helv. 52 (1977), 457–81.CrossRefGoogle Scholar
11Würgler, U.. Commutative ring spectra of characteristic 2. Cosmment. Math. Helv. 61 (1986), 33–45.CrossRefGoogle Scholar