Remote Access Proceedings of the American Mathematical Society
Green Open Access

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
Full-text PDF

Abstract | References | Similar Articles | Additional Information

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 [Enhancements On Off] (What's this?)

  • 1. Manfred Dugas, Adolf Mader, and Charles Vinsonhaler, Large E-rings exist., J. Algebra 108 (1987), 88 - 101. MR 0887193 (88e:16047)
  • 2. Theodore G. Faticoni, Each countable reduced torsion-free commutative ring is a pure subring of an E-ring., Commun. Algebra 15 (1987), 2545 - 2564. MR 0917754 (88i:20078)
  • 3. Rüdiger Göbel and Jan Trlifaj, Endomorphism algebras and approximations of modules, Walter de Gruyter Verlag, Berlin, to appear, 2005.
  • 4. Rüdiger Göbel and Simone L. Wallutis, An algebraic version of the strong black box, Algebra and Discrete Mathematics, 1 (3) (2003) 7 - 45. MR 2048638
  • 5. P. Schultz, The endomorphism ring of the additive group of a ring., J. Aust. Math. Soc. 15 (1973), 60 - 69. MR 0338218 (49:2984)

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (2000): 16W20, 16D70

Retrieve articles in all journals with MSC (2000): 16W20, 16D70


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.

American Mathematical Society