Endomorphism rings of p-local finite spectra are semi-perfect
Published online by Cambridge University Press: 26 May 2009
Abstract
Let X be a finite spectrum. We prove that R(X(p)), the endomorphism ring of the p-localization of X, is a semi-perfect ring. This implies, among other things, a strong form of unique factorization for finite p-local spectra. The main step in the proof is that the Jacobson radical of R(X(p)) is idempotent-lifting, which is proved by a combination of geometric properties of finite spectra and algebraic properties of the p-localization.
- Type
- Research Article
- Information
- Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 139 , Issue 3 , June 2009 , pp. 567 - 574
- Copyright
- Copyright © Royal Society of Edinburgh 2009
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