Quasi-balanced torsion-free groups
Goeters, H. Pat ; Ullery, William
Commentationes Mathematicae Universitatis Carolinae, Tome 39 (1998), p. 431-443 / Harvested from 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.

Publié le : 1998-01-01
Classification:  20K15,  20K25,  20K27,  20K35,  20K40 
@article{119022,
     author = {H. Pat Goeters and William Ullery},
     title = {Quasi-balanced torsion-free groups},
     journal = {Commentationes Mathematicae Universitatis Carolinae},
     volume = {39},
     year = {1998},
     pages = {431-443},
     zbl = {0968.20027},
     mrnumber = {1666837},
     language = {en},
     url = {http://dml.mathdoc.fr/item/119022}
}

Goeters, H. Pat; Ullery, William. Quasi-balanced torsion-free groups. Commentationes Mathematicae Universitatis Carolinae, Tome 39 (1998) pp. 431-443. http://gdmltest.u-ga.fr/item/119022/

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