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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Homological algebra and set theory


Author: Paul C. Eklof
Journal: Trans. Amer. Math. Soc. 227 (1977), 207-225
MSC: Primary 02K05; Secondary 20K35, 02K25, 04A20
MathSciNet review: 0453520
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Abstract: Assuming the Axiom of Constructibility, necessary and sufficient conditions are given for the vanishing of $ {\operatorname{Ext}}_\Lambda ^1$ for rings $ \Lambda $ of global dimension 1. Using Martin's Axiom, the necessity of these conditions is shown not to be a theorem of ZFC. Applications are given to abelian group theory, including a partial solution (assuming $ {\text{V}} = {\text{L}}$) to a problem of Baer on the splitting of abelian groups. Some independence results in abelian group theory are also proved.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9947-1977-0453520-X
PII: S 0002-9947(1977)0453520-X
Article copyright: © Copyright 1977 American Mathematical Society



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