A note on quasi-isomorphism of torsion free abelian groups of finite rank
نویسندگان
چکیده
منابع مشابه
The Classification of Torsion-free Abelian Groups of Finite Rank up to Isomorphism and up to Quasi-isomorphism
We prove that the isomorphism and quasi-isomorphism relations on the p-local torsion-free abelian groups of fixed finite rank n are incomparable with respect to Borel reducibility.
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Let RA be a group ring of an abelian group A and let I be an ideal of RA . We say that a subgroup B of A controls I if I = (I ∩ RB)RA. The intersection c(I) of all subgroups of A controlling I is said to be the controller of the ideal I ; c(I) is the minimal subgroup of A which controls the ideal I . The ideal I is said to be faithful if I = A ∩ (1 + I) = 1. In theorem 4 we consider some method...
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In 1937, Baer [5] introduced the notion of the type of an element in a torsion-free abelian group and showed that this notion provided a complete invariant for the classification problem for torsion-free abelian groups of rank 1. Since then, despite the efforts of such mathematicians as Kurosh [23] and Malcev [25], no satisfactory system of complete invariants has been found for the torsion-fre...
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In 1937, Baer solved the classification problem for the torsion-free abelian groups of rank 1. Since then, despite the efforts of many mathematicians, no satisfactory solution has been found of the classification problem for the torsion-free abelian groups of rank n ≥ 2. So it is natural to ask whether the classification problem for the higher rank groups is genuinely difficult. In this article...
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ژورنال
عنوان ژورنال: Czechoslovak Mathematical Journal
سال: 1965
ISSN: 0011-4642,1572-9141
DOI: 10.21136/cmj.1965.100648