Baer’s lemma and Fuchs’s problem 84a
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- by Ulrich Albrecht PDF
- Trans. Amer. Math. Soc. 293 (1986), 565-582 Request permission
Abstract:
An indecomposable, torsion-free, reduced abelian group $A$ has the properties that (i) each subgroup $B$ of an $A$-projective group with ${S_A}(B) = B$ is $A$-projective and (ii) each subgroup $B$ of a group $G$ with ${S_A}(G) + B = G$ and $G/B$ $A$-projective is a direct summand if and only if $A$ is self-small and flat as a left $E(A)$-module, and $E(A)$ is right hereditary. Furthermore, a group-theoretic characterization is given for torsion-free, reduced abelian groups with a right and left Noetherian, hereditary endomorphism ring. This is applied to Fuchs’ Problem 84a. Finally, various applications of the results of this paper are given.References
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Additional Information
- © Copyright 1986 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 293 (1986), 565-582
- MSC: Primary 20K20; Secondary 16A50, 16A65, 20K30
- DOI: https://doi.org/10.1090/S0002-9947-1986-0816310-7
- MathSciNet review: 816310