Abstract. B(1)-groups are a class of torsionfree Abelian groups of finite rank, part of the main class of Butler groups. In the paper C. Metelli, On direct sums of B(1)-groups, Comment. Math. Univ. Carolinae 34 (1993), 587–591, the problem of direct sums of B(1)-groups was discussed, and a necessary and sufficient condition was given for the direct sum of two B(1)-groups to be a B(1)-group. While sufficiency holds, necessity was wrongly claimed; we solve here the problem, and in the process study a curious hierarchy among indecomposable direct summands of B(1)-groups.
On direct sums of B(1)-groups--II / DE VIVO, Clorinda; Metelli, Claudia. - In: COMMENTATIONES MATHEMATICAE UNIVERSITATIS CAROLINAE. - ISSN 0010-2628. - STAMPA. - 47:2(2006), pp. 189-202.
On direct sums of B(1)-groups--II
DE VIVO, CLORINDA;METELLI, CLAUDIA
2006
Abstract
Abstract. B(1)-groups are a class of torsionfree Abelian groups of finite rank, part of the main class of Butler groups. In the paper C. Metelli, On direct sums of B(1)-groups, Comment. Math. Univ. Carolinae 34 (1993), 587–591, the problem of direct sums of B(1)-groups was discussed, and a necessary and sufficient condition was given for the direct sum of two B(1)-groups to be a B(1)-group. While sufficiency holds, necessity was wrongly claimed; we solve here the problem, and in the process study a curious hierarchy among indecomposable direct summands of B(1)-groups.| File | Dimensione | Formato | |
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