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Algebra Discrete Math., 2003, Issue 3, Pages 7–45 (Mi adm382)  

This article is cited in 10 scientific papers (total in 10 papers)

An algebraic version of the Strong Black Box

Rüdiger Göbel, Simone L. Wallutis

FB 6 – Mathematik, Universität Duisburg-Essen, 45117 Essen, Germany

Abstract: Various versions of the prediction principle called the “Black Box” are known. One of the strongest versions can be found in [EM]. There it is formulated and proven in a model theoretic way. In order to apply it to specific algebraic problems it thus has to be transformed into the desired algebraic setting. This requires intimate knowledge on model theory which often prevents algebraists to use this powerful tool. Hence we here want to present algebraic versions of this“Strong Black Box” in order to demonstrate that the proofs are straightforward and that it is easy enough to change the setting without causing major changes in the relevant proofs. This shall be done by considering three different applications where the obtained results are actually known.

Keywords: prediction principle, Black Box, endomorphism algebra, $E$-ring, $E(R)$-algebra, ultra-cotorsion-free module.

Full text: PDF file (401 kB)

Bibliographic databases:
MSC: 03E75, 20K20, 20K30, 13C99
Received: 23.05.2003
Revised: 13.11.2003
Language:

Citation: Rüdiger Göbel, Simone L. Wallutis, “An algebraic version of the Strong Black Box”, Algebra Discrete Math., 2003, no. 3, 7–45

Citation in format AMSBIB
\Bibitem{GobWal03}
\by R\"udiger~G\"obel, Simone~L.~Wallutis
\paper An algebraic version of the Strong Black Box
\jour Algebra Discrete Math.
\yr 2003
\issue 3
\pages 7--45
\mathnet{http://mi.mathnet.ru/adm382}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=2048638}
\zmath{https://zbmath.org/?q=an:1067.03061}


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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. Dugas M., “Localizations of Torsion-Free Abelian Groups II”, J. Algebra, 284:2 (2005), 811–823  crossref  mathscinet  zmath  isi  scopus
    2. Fuchs L., Gobel R., “Large Superdecomposable E(R)-Algebras”, Fundam. Math., 185:1 (2005), 71–82  crossref  mathscinet  zmath  isi
    3. Braun G., Gobel R., “E-Algebras Whose Torsion Part Is Not Cyclic”, Proc. Amer. Math. Soc., 133:8 (2005), 2251–2258  crossref  mathscinet  zmath  isi  scopus
    4. Buckner J., Dugas M., “Co-Local Subgroups of Abelian Groups”, Abelian Groups, Rings, Modules, and Homological Algebra, Monographs and Textbooks in Pure and Applied Mathematics, 249, eds. Goeters P., Jenda O., 2006, 29–37  mathscinet  zmath  isi
    5. Buckner J., Dugas M., “Quasi-Co-Local Subgroups of Abelian Groups”, J. Pure Appl. Algebr., 211:2 (2007), 392–399  crossref  mathscinet  zmath  isi  scopus
    6. Buckner J., Dugas M., “Quasi-Localizations of Z”, Isr. J. Math., 160:1 (2007), 349–370  crossref  mathscinet  zmath  isi  scopus
    7. Dugas M., “Co-Local Subgroups of Abelian Groups II”, J. Pure Appl. Algebr., 208:1 (2007), 117–126  crossref  mathscinet  zmath  isi  scopus
    8. Goebel R., Rodriguez J.L., Struengmann L., “Cellular Covers of Cotorsion-Free Modules”, Fundam. Math., 217:3 (2012), 211–231  crossref  mathscinet  zmath  isi  scopus
    9. Goebel R., Herden D., Shelah S., “Prescribing Endomorphism Algebras of Aleph(N)-Free Modules”, J. Eur. Math. Soc., 16:9 (2014), 1775–1816  crossref  mathscinet  zmath  isi
    10. Fuchs L., “Abelian Groups”, Abelian Groups, Springer Monographs in Mathematics, Springer, 2015, 1–747  crossref  mathscinet  isi
  • Algebra and Discrete Mathematics
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