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 -algebras whose torsion part is not cyclic
Author(s):
Gábor
Braun;
Rüdiger
Göbel
Journal:
Proc. Amer. Math. Soc.
133
(2005),
2251-2258.
MSC (2000):
Primary 16W20;
Secondary 16D70
Posted:
March 15, 2005
MathSciNet review:
2138867
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Abstract:
We consider algebras  over a Dedekind domain  with the property  and generalize Schultz' structure theory of the case  to Dedekind domains. We construct examples of mixed  -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  .
References:
-
- 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)
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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:
10.1090/S0002-9939-05-07815-9
PII:
S 0002-9939(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
Posted:
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 of article:
Copyright
2005,
American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.
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