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Commutative ring-spectra of characteristic 2. (English) Zbl 0622.55003

Let E be a commutative ring-spectrum with \(\pi_*(E)\) of characteristic 2. The author proves that there is an equivalence of ring theories \(E^*(-)\cong H^*(-; E^*)\) on the category of CW-spectra. The proof proceeds by an induction on the Postnikov factors of E and uses a property of the products of the spectra P(n). The above result yields an elegant proof for the fact that the Eilenberg-MacLane spectrum \(K({\mathbb{Z}}_ 2,0)\) is a Thom spectrum over \(\Omega^ 2S^ 3\).
Reviewer: R.Kultze

MSC:

55N20 Generalized (extraordinary) homology and cohomology theories in algebraic topology
55P45 \(H\)-spaces and duals
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