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A Note on the Square Subgroups of Decomposable Torsion-Free Abelian Groups of Rank Three
Annales Mathematicae Silesianae, 2018 A hypothesis stated in [16] is confirmed for the case of associative rings. The answers to some questions posed in the mentioned paper are also given. The square subgroup of a completely decomposable torsion-free abelian group is described (in both cases
Woronowicz Mateusz
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Indecomposable decompositions of torsion-free abelian groups [PDF]
Journal of Algebra, 2018 An indecomposable decomposition of a torsion-free abelian group $G$ of rank $n$ is a decomposition $G=A_1\oplus\cdots\oplus A_t$ where $A_i$ is indecomposable of rank $r_i$ so that $\sum_i r_i=n$ is a partition of $n$. The group $G$ may have decompositions that result in different partitions of $n$.
Adolf Mader, Phill Schultz
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International Journal of Mathematics and Mathematical Sciences, 2003 Let p be a prime. It is shown that an automorphism α of an abelian p-group A lifts to any abelian p-group of which A is a homomorphic image if and only if α=π idA, with π an invertible p-adic integer.
S. Abdelalim, H. Essannouni
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Separable torsion-free abelian E∗-groups
Journal of Pure and Applied Algebra, 1998 The first half of this paper characterizes the torsion-free separable abelian groups \(G\) whose endomorphism semigroup \(E(G)^*\) admits a unique addition; that is, the endomorphism ring \(E(G)\) is isomorphic to any ring \(S\) for which \(E(G)^*\) is isomorphic to \(S^*\).
Lubimcev, O. +2 more
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On Weakly Transitive Torsion-Free Abelian Groups
Journal of Mathematical Sciences, 2021 This short note adds new information on a previous paper with the same subject by \textit{B. Goldsmith} and \textit{L. Strüngmann} [Commun. Algebra 33, No. 4, 1177--1191 (2005; Zbl 1142.20032)]. The results are: Proposition 2. If \(A\) is a reduced torsion-free group with strongly indecomposable pure subgroups and the set \(T(A)\) of types of all its ...
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Annihilator equivalence of torsion-free abelian groups [PDF]
Journal of the Australian Mathematical Society. Series A. Pure Mathematics and Statistics, 1992 AbstractWe define an equivalence relation on the class of torsion-free abelian groups under which two groups are equivalent ifevery pure subgroup of one has a non-zero image in the other, and each has a non-zero image in every torsion-free factor of the other.We study the closure properties of the equivalence classes, and the structural properties of ...
Schultz, P. +2 more
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Torsion-free abelian groups are Borel complete
Annals of Mathematics, 2018 We prove that the Borel space of torsion-free Abelian groups with domain $ω$ is Borel complete, i.e., the isomorphism relation on this Borel space is as complicated as possible, as an isomorphism relation. This solves a long-standing open problem in descriptive set theory, which dates back to the seminal paper on Borel reducibility of Friedman and ...
Paolini G., Shelah S.
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Characterizing group C*-algebras through their unitary groups: the Abelian case [PDF]
, 2010 We study to what extent group C*-algebras are characterized by their unitary groups. A complete characterization of which Abelian group C*-algebras have isomorphic unitary groups is obtained. We compare these results with other unitary-related invariants
Galindo, Jorge +1 more
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Finitely generated abelian groups of units [PDF]
, 2019 In 1960 Fuchs posed the problem of characterizing the groups which are the groups of units of commutative rings. In the following years, some partial answers have been given to this question in particular cases.
Del Corso, Ilaria
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Almost completely decomposable torsion free abelian groups [PDF]
Proceedings of the American Mathematical Society, 1974 A finite rank torsion free abelian group G G is almost completely decomposable if there exists a completely decomposable subgroup C C with finite index in G G . The minimum of [ G : C ] [G:C] over all completely decomposable subgroups C
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