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Title: Quasi-balanced torsion-free groups (English)
Author: Goeters, H. Pat
Author: Ullery, William
Language: English
Journal: Commentationes Mathematicae Universitatis Carolinae
ISSN: 0010-2628 (print)
ISSN: 1213-7243 (online)
Volume: 39
Issue: 3
Year: 1998
Pages: 431-443
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Category: math
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Summary: An exact sequence $0\to A\to B\to C\to 0$ of torsion-free abelian groups is quasi-balanced if the induced sequence $$ 0\to \bold Q\otimes\operatorname{Hom}(X,A)\to\bold Q\otimes\operatorname{Hom}(X,B) \to\bold Q\otimes\operatorname{Hom}(X,C)\to 0 $$ is exact for all rank-1 torsion-free abelian groups $X$. This paper sets forth the basic theory of quasi-balanced sequences, with particular attention given to the case in which $C$ is a Butler group. The special case where $B$ is almost completely decomposable gives rise to a descending chain of classes of Butler groups. This chain is a generalization of the chain of Kravchenko classes that arise from balanced sequences. As an application of our results concerning quasi-balanced sequences, the relationship between the two chains in the quasi-category of torsion-free abelian groups is illuminated. (English)
Keyword: quasi-balanced
Keyword: almost balanced
Keyword: Kravchenko classes
MSC: 20K15
MSC: 20K25
MSC: 20K27
MSC: 20K35
MSC: 20K40
idZBL: Zbl 0968.20027
idMR: MR1666837
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Date available: 2009-01-08T18:45:03Z
Last updated: 2012-04-30
Stable URL: http://hdl.handle.net/10338.dmlcz/119022
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Reference: [A1] Arnold D.: Pure subgroups of finite rank completely decomposable groups.Abelian Group Theory Lecture Notes in Math. 874 Springer-Verlag New York (1982), 1-31. MR 0645913
Reference: [A2] Arnold D.: Finite Rank Torsion-Free Abelian Groups and Rings.Lecture Notes in Math. 931 Springer-Verlag New York (1982). Zbl 0493.20034, MR 0665251
Reference: [AV] Arnold D., Vinsonhaler C.: Pure subgroups of finite rank completely decomposable groups $anII$.Abelian Group Theory Lecture Notes in Math. 1006 Springer-Verlag New York (1983), 97-143. MR 0722614
Reference: [B] Butler M.C.R.: A class of torsion-free abelian groups of finite rank.Proc. London Math. Soc. 15 (1965), 680-698. Zbl 0131.02501, MR 0218446
Reference: [F] Fuchs L.: Infinite Abelian Groups.II Academic Press New York (1973). Zbl 0257.20035, MR 0349869
Reference: [K] Kravchenko A.A.: Balanced and cobalanced Butler groups.Math. Notes Acad. Sci. USSR 45 (1989), 369-373. Zbl 0695.20032, MR 1005459
Reference: [NV1] Nongxa L.G., Vinsonhaler C.: Balanced Butler groups.J. Algebra, to appear. Zbl 0846.20060, MR 1378545
Reference: [NV2] Nongxa L.G., Vinsonhaler C.: Balanced representations of partially ordered sets.to appear.
Reference: [V] C. Vinsonhaler: A survey of balanced Butler groups and representations.Abelian Groups and Modules Lecture Notes in Pure and Applied Math. 182 Marcel Dekker (1996), 113-122. Zbl 0865.20040, MR 1415625
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