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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

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

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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A dual to Baer’s lemma
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by Ulrich Albrecht and H. Pat Goeters PDF
Proc. Amer. Math. Soc. 105 (1989), 817-826 Request permission

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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Additional Information
  • © Copyright 1989 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 105 (1989), 817-826
  • MSC: Primary 20K40
  • DOI: https://doi.org/10.1090/S0002-9939-1989-0963569-X
  • MathSciNet review: 963569