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Torsion-free abelian groups revisited [PDF]
Rendiconti del Seminario Matematico della Università di Padova, 2019 Let G be a torsion--free abelian group of finite rank. The automorphism group Aut(G) acts on the set of maximal independent subsets of G. The orbits of this action are the isomorphism classes of indecomposable decompositions of G. G contains a direct sum
P. Schultz
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A Note on the Square Subgroups of Decomposable Torsion-Free Abelian Groups of Rank Three [PDF]
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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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 ...
A. Chekhlov
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Torsion-Free Abelian Group Rings III
Bulletin of the Faculty of Science, Ibaraki University. Series A, Mathematics, 1977 Ryuki Matsuda
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Filial rings on direct sums and direct products of torsion-free abelian groups
Чебышевский сборник, 2021 A ring whose additive group coincides with an abelian group 𝐺 is called a ring on 𝐺 . An abelian group 𝐺 is called a 𝑇𝐼 -group if every associative ring on 𝐺 is filial. If every (associative) ring on an abelian group 𝐺 is an 𝑆𝐼 -ring (a hamiltonian ring),
E. Kompantseva +2 more
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On the Indecomposability of Torsion-Free Abelian Groups [PDF]
Proceedings of the American Mathematical Society, 1965 1. We consider the following question posed by E. Weinberg [4, ?5.2]: Does there exist a torsion-free abelian group of cardinality greater than the continuum (K) with the property that each pure subgroup is (directly) indecomposable? In ?2 we answer this question negatively for a large class of groups which contains, most notably, the class of ...
Josh Armstrong
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On Undecidability of Finite Subsets Theory for Torsion Abelian Groups
Mathematics, 2022 Let M be a commutative cancellative monoid with an element of infinite order. The binary operation can be extended to all finite subsets of M by the pointwise definition. So, we can consider the theory of finite subsets of M.
Sergey Mikhailovich Dudakov
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Regularity in torsion-free abelian groups [PDF]
Czechoslovak Mathematical Journal, 1992 Eine Untergruppe \(B\) einer torsionsfreien abelschen Gruppe \(A\) heißt regulär (kritisch regulär) falls \(t^ B(b) = t^ A(b)\) für alle \(b\in B\) (falls für alle Typen \(t\) gilt: \(B(t) \setminus B^*(t)_ * \subset A(t)\setminus A^*(t)_ *\)). Die Untergruppe \(B\) heißt stark regulär, falls \(B\) eine reguläre und eine kritisch reguläre Untergruppe ...
Müller, Edgar, Mutzbauer, Otto
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Invariants for a class of torsion-free abelian groups [PDF]
Proceedings of the American Mathematical Society, 1989 In this note we present a complete set of quasi-isomorphism invariants for strongly indecomposable abelian groups of the form G = G ( A 1 , … , A n ) G = G({A_1}, \ldots ,{A_n}) .
Arnold, D., Vinsonhaler, C.
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On Some Results of a Torsion-Free Abelian Kernel Group
Recoletos Multidisciplinary Research Journal, 2014 In [6], for any torsion-free abelian groups Gand H, the kernel of Hin GisfHGGHHomfker, ker,. The kernel of Hin Gis a pure fully invariant subgroup of G.
Ricky B. Villeta
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