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Rings on Abelian torsion-free groups of finite rank [PDF]

Beitrage Zur Algebra Und Geometrie, 2021
In the class of reduced Abelian torsion-free groups $G$ of finite rank, we describe TI-groups, this means that every associative ring on $G$ is filial. If every associative multiplication on $G$ is the zero multiplication, then $G$ is called a $nil_a$-group.
E I Kompantseva, A A Tuganbaev, Kompantseva E I   +2 more
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Summands of finite rank torsion free abelian groups

Journal of Algebra, 1974
AbstractA finite rank torsion free abelian group has, up to isomorphism, only finitely many summands.
E L Lady
exaly   +3 more sources

Duality of the categories of torsion-free Abelian groups of finite rank and quotient divisible Abelian groups

Journal of Mathematical Sciences, 2010
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Yakovlev A V
exaly   +4 more sources

Multiplication Groups of Abelian Torsion-Free Groups of Finite Rank

Mediterranean Journal of Mathematics, 2023
For an Abelian group $G$, any homomorphism $μ\colon G\otimes G\rightarrow G$ is called a \textsf{multiplication} on $G$. The set $\text{Mult}\,G$ of all multiplications on an Abelian group $G$ itself is an Abelian group with respect to addition; the group is called the \textsf{multiplication group} of $G$.
E. I. Kompantseva, A. A. Tuganbaev
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Torsion-Free Abelian Groups of Finite Rank with Marked Bases

Journal of Mathematical Sciences, 2021
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
A. Fomin
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Hypertypes of torsion-free abelian groups of finite rank [PDF]

Bulletin of the Australian Mathematical Society, 1989
Let G be a torsion-free abelian group of finite rank n and let F be a full free subgroup of G. Then G/F is isomorphic to T1 ⊕ … ⊕ Tn, where T1 ⊆ T2 ⊆ … ⊆ Tn ⊆ ℚ/ℤ. It is well known that type T1 = inner type G and type Tn = outer type G. In this note we give two characterisations of type Ti for 1 < i < n.
Goeters, H. P., Vinsonhaler, C., Wickless, W.   +2 more
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Strongly homogeneous torsion free abelian groups of finite rank [PDF]

Proceedings of the American Mathematical Society, 1976
An abelian group is strongly homogeneous if for any two pure rank 1 subgroups there is an automorphism sending one onto the other. Finite rank torsion free strongly homogeneous groups are characterized as the tensor product of certain subrings of algebraic number fields with finite direct ...
D. Arnold
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Finite Rank Torsion Free Abelian Groups and Rings

Lecture Notes in Mathematics, 1982
David M Arnold
exaly   +3 more sources

The classification problem for torsion-free abelian groups of finite rank [PDF]

Journal of the American Mathematical Society, 2002
We prove that for each n ≥ 1
S. Thomas
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A note on torsion-free abelian groups of finite rank [PDF]

Proceedings of the American Mathematical Society, 1973
Let G be a torsion-free abelian group of rank n and X= {xl, *. , x,j a maximal set of rationally independent elements in G. It is well known that any g e G can be uniquely written g= oc1xl?+ +x, for some cci, . , ?C72, E Q, the rational numbers. This enables us to define, for any such (G, X), a collection of subgroups of Q and "natural" isomorphisms ...
Wickless, W., Vinsonhaler, C.
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