Homological algebra and set theory

Eklof, Paul C.

doi:10.1090/S0002-9947-1977-0453520-X

Homological algebra and set theory
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by Paul C. Eklof PDF

Trans. Amer. Math. Soc. 227 (1977), 207-225 Request permission

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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20

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