Quasi-balanced torsion-free groups

Goeters, H. Pat ; Ullery, William

Commentationes Mathematicae Universitatis Carolinae, Tome 39 (1998) no. 3, pp. 431-443.

Résumé

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.

Détail

Classification : 20K15, 20K25, 20K27, 20K35, 20K40
Keywords: quasi-balanced; almost balanced; Kravchenko classes