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Algebra and Discrete Mathematics, 2003, Issue 3, Pages 7–45
(Mi adm382)
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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.
Received: 23.05.2003 Revised: 13.11.2003
Citation:
Rüdiger Göbel, Simone L. Wallutis, “An algebraic version of the Strong Black Box”, Algebra Discrete Math., 2003, no. 3, 7–45
Linking options:
https://www.mathnet.ru/eng/adm382 https://www.mathnet.ru/eng/adm/y2003/i3/p7
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Abstract page: | 239 | Full-text PDF : | 68 | First page: | 1 |
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