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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

A dual to Baer's lemma


Authors: Ulrich Albrecht and H. Pat Goeters
Journal: Proc. Amer. Math. Soc. 105 (1989), 817-826
MSC: Primary 20K40
MathSciNet review: 963569
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Abstract: Let $ A$ be an abelian group. We investigate the splitting of sequences $ ( * )\quad 0 \to P \to G \to H \to 0$ with $ P\quad A$-projective: Examples show that restrictions on $ G$ and $ H$ must be imposed to obtain a dual to Baer's Lemma. A characterization of the splitting of sequences like (*) where $ G$ is $ A$-reflexive and $ {R_A}\left( H \right) = 0$ is given in terms of $ A$ and $ E\left( A \right)$, when $ A$ is slender and nonmeasurable. Furthermore, we consider related problems and present applications of our results.


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DOI: https://doi.org/10.1090/S0002-9939-1989-0963569-X
Keywords: Endomorphism ring, Baer's Lemma, hereditary, splitting sequence
Article copyright: © Copyright 1989 American Mathematical Society