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Proceedings of the American Mathematical Society

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

 
 

 

$E$-algebras whose torsion part is not cyclic


Authors: Gábor Braun and Rüdiger Göbel
Journal: Proc. Amer. Math. Soc. 133 (2005), 2251-2258
MSC (2000): Primary 16W20; Secondary 16D70
DOI: https://doi.org/10.1090/S0002-9939-05-07815-9
Published electronically: March 15, 2005
MathSciNet review: 2138867
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Abstract: 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

DOI: https://doi.org/10.1090/S0002-9939-05-07815-9
Keywords: Mixed $E$-rings, Dedekind domain
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
Article copyright: © Copyright 2005 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.