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Direct summands of direct products of slender modules. (English) Zbl 0532.13007

Suppose \(P=\prod_{I}G_ i\) is a direct product of slender R-modules. If \(| I|\) is non-measurable and A is a direct summand of P, then \(A=\prod_{J}A_ j\) where each \(A_ j\) is isomorphic to a direct summand of a countable direct product of \(G_ i's\). If \(R={\mathbb{Z}}\) and P is a torsion-free reduced abelian group, then, if each \(G_ i\) has rank one, A is a direct product of rank one groups.

MSC:

13C05 Structure, classification theorems for modules and ideals in commutative rings
20K25 Direct sums, direct products, etc. for abelian groups
20K15 Torsion-free groups, finite rank
13C13 Other special types of modules and ideals in commutative rings
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