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Endomorphism rings of p-local finite spectra are semi-perfect

Published online by Cambridge University Press:  26 May 2009

Petar Pavešić
Petar Pavešić
Affiliation:
Fakulteta za Matematiko in Fiziko, Univerza v Ljubljani, Jadranska 19, 1111 Ljubljana, Slovenia ([email protected])
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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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