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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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$E$-algebras whose torsion part is not cyclic
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by Gábor Braun and Rüdiger Göbel PDF
Proc. Amer. Math. Soc. 133 (2005), 2251-2258 Request permission


We consider algebras $A$ over a Dedekind domain $R$ with the property $A \cong \operatorname {EndAlg}_R A$ and generalize Schultz’ structure theory of the case $R=\mathbb {Z}$ to Dedekind domains. We construct examples of mixed $E(R)$-algebras, which are non-split extensions of the submodule of elements infinitely divisible by the relevant prime ideals. This is also new in the case $R=\mathbb {Z}$.
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Additional Information
  • Gábor Braun
  • Affiliation: Alfréd Rényi Institute of Mathematics, Hungarian Academy of Sciences, Budapest, Reáltanoda u 13-15, 1053 Hungary
  • Rüdiger Göbel
  • Affiliation: Fachbereich 6, Mathematik, Universität Duisburg-Essen, Universitätsstrasse 3, 45117, Germany
  • Received by editor(s): February 17, 2003
  • Received by editor(s) in revised form: July 22, 2003, and April 20, 2004
  • Published electronically: March 15, 2005
  • Additional Notes: This work was supported by the project No. I-706-54.6/2001 of the German-Israeli Foundation for Scientific Research & Development.
  • Communicated by: Bernd Ulrich
  • © Copyright 2005 American Mathematical Society
    The copyright for this article reverts to public domain 28 years after publication.
  • Journal: Proc. Amer. Math. Soc. 133 (2005), 2251-2258
  • MSC (2000): Primary 16W20; Secondary 16D70
  • DOI:
  • MathSciNet review: 2138867