$E$-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
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 $R=\mathbb {Z}$.References
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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: https://doi.org/10.1090/S0002-9939-05-07815-9
- MathSciNet review: 2138867