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Self-splitting Abelian groups

Published online by Cambridge University Press:  17 April 2009

P. Schultz
P. Schultz
Affiliation:
Department of Mathematics and Statistics, The University of Western Australia, Nedlands W.A. 6907, Australia, e-mail: [email protected]
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Abstract

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G is reduced torsion-free A belian group such that for every direct sum ⊕G of copies of G, Ext(⊕G, ⊕G) = 0 if and only if G is a free module over a rank 1 ring. For every direct product ΠG of copies of G, Ext(ΠG,ΠG) = 0 if and only if G is cotorsion.

This paper began as a Research Report of the Department of Mathematics of the University of Western Australia in 1988, and circulated among members of the Abelian group community. However, it was never submitted for publication. The results have been cited, widely, and since copies of the original research report are no longer available, the paper is presented here in its original form in Sections 1 to 5. In Section 6, I survey the progress that has been made in the topic since 1988.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 64 , Issue 1 , August 2001 , pp. 71 - 79
Copyright
Copyright © Australian Mathematical Society 2001

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