Geodesic
Quasi-balanced torsion-free groups
Commentationes Mathematicae Universitatis Carolinae, Tome 39 (1998) no. 3, pp. 431-443 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

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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.
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.
Classification : 20K15, 20K25, 20K27, 20K35, 20K40
Keywords: quasi-balanced; almost balanced; Kravchenko classes 
@article{CMUC_1998_39_3_a0,
     author = {Goeters, H. Pat and Ullery, William},
     title = {Quasi-balanced torsion-free groups},
     journal = {Commentationes Mathematicae Universitatis Carolinae},
     pages = {431--443},
     year = {1998},
     volume = {39},
     number = {3},
     mrnumber = {1666837},
     zbl = {0968.20027},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/CMUC_1998_39_3_a0/}
}
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Goeters, H. Pat; Ullery, William. Quasi-balanced torsion-free groups. Commentationes Mathematicae Universitatis Carolinae, Tome 39 (1998) no. 3, pp. 431-443. http://geodesic.mathdoc.fr/item/CMUC_1998_39_3_a0/