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- W4230674799 abstract "Let $A$ be a finite rank, indecomposable torsion-free Abelian group whose $p$-ranks are less than two for all primes $p$. Let $G$ be a direct product of copies of $A$, and $B$ be a nonzero countable pure subgroup of $G$ such that $B$ is the span of the homomorphic images of $A$ in $B$. Then it is shown that $B$ is a direct sum of copies of $A$. This result is applied to obtain a Krull-Schmidt theorem for direct sums of groups $A$ from a semirigid class of groups. In particular, if the groups $A$ have rank one, then the well-known BaerKulikov-Kaplansky theorem is obtained." @default.
- W4230674799 created "2022-05-11" @default.
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- W4230674799 date "1973-04-01" @default.
- W4230674799 modified "2023-09-26" @default.
- W4230674799 title "Direct Products and Sums of Torsion-Free Abelian Groups" @default.
- W4230674799 doi "https://doi.org/10.2307/2039268" @default.
- W4230674799 hasPublicationYear "1973" @default.
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