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Results in Mathematics

, Volume 17, Issue 3–4, pp 179–201 | Cite as

Endomorphism Rings of Faithfully Flat Abelian Groups

  • Ulrich Albrecht
Article

abstract

We discuss faithfully flat abelian groups in conjunction with the following: A class C of abelian groups with full A-socle is A-balanced closed if it is closed with respect to finite direct sums and subgroups with full A-socle, ker ϕ ε C for all ϕ ε Horn (G, H) and G, H ε C, and A is projective with respect to all exact sequences of elements of C. A self-small group A admits an A-balanced closed class C which contains ⊕IA for all index-sets I exactly if it is faithfully flat as an E(A)-module. We show that Corner's as well as Dugas' and Göbel's realization theorems yield abelian groups that are faithfully flat as E(A)-modules. Several applications of these results are given, some of which yield an answer to part a of Fuchs' Problem 84 and a partial respond to part c of the same problem.

1980 Mathematics Subject Classifications

20K20 20K30 16A65 20K25 16A50 

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Copyright information

© Birkhäuser Verlag, Basel 1990

Authors and Affiliations

  • Ulrich Albrecht
    • 1
  1. 1.Department of Algebra, Combinatorics and Analysis 120 Mathematics AnnexAuburn UniversityAuburnUSA

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