Results 141 to 150 of about 24,182 (180)

Extensions of torsion-free Abelian groups of finite rank

Archiv der Mathematik, 1972
R. Warfield
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Torsion-free abelian α-irreducible groups of finite rank

Communications in Algebra, 1994
If F is a free abelian group of finite rank and α is an endomorphism or an automorphism of its divisible hull, then the α‐ hull is determined, i.e. the minimal torsion-free abelian group with this endomorphism a. Torsion-free abelian groups of finite rank are called α-irreducible if their divisible hull is α-irreducible for an automorphism a.
Alexander A. Fomin, Otto Mutzbauer
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New examples of indecomposable torsion-free abelian groups of finite rank and rings on them

Journal of Algebra and its Applications, 2022
Ryszard Andruszkiewicz, Mateusz Woronowicz   +1 more
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E-Uniserial Torsion-Free Abelian Groups of Finite Rank

1984
An abelian group A is said to be E-uniserial if the lattice of fully invariant subgroups of A is a chain.
J. Hausen
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On quasidecomposable finite rank torsion-free Abelian groups

Siberian Mathematical Journal, 1998
The author obtains two types of quasidecompositions for a finite rank torsion-free Abelian group \(G\). Using them, he proves pure semisimplicity of the module \(_EG\) in a particular case and obtains a criterion for pure semisimplicity of the module \(_EG\) in the general case.
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On the torsion-free ranks of finitely generated nilpotent groups and of their abelian subgroups [PDF]

Journal of Group Theory, 2004
Denote by \(f(n)\) the greatest integer \(h\) such that there exists a finitely generated nilpotent group of torsion-free rank \(h\) such that the torsion-free ranks of all Abelian subgroups of this group are not greater than \(n\). The author proves that the function \(f(n)\) satisfies the inequality \(f(n)\geq\tfrac18(n^2-4)+n\). Proving this theorem,
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Categories of Mixed and Torsion-Free Finite Rank Abelian Groups [PDF]

, 1995
In this paper “group” always means “abelian group”. For a group G let T = T(G) be the torsion part and, for a prime p, let T p = T p (G), be the p-torsion part of G.
Alexander Fomin, W. Wickless
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Self-Cancellation of Torsion-Free Abelian Groups of Finite Rank

Journal of Mathematical Sciences, 2002
An Abelian group \(A\) is said to have self-cancellation if \(A\oplus A\cong A\oplus B\) implies \(A\cong B\). A very simple example of a rank 4 torsion-free Abelian group without the self-cancellation property is constructed. The construction is based on the author's criterion [Algebra Anal. 7, No. 6, 33-78 (1995); corrections ibid. 11, No. 4, 222-224
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Direct decompositions of torsion-free homogeneous Abelian groups of finite rank

Lithuanian Mathematical Journal, 1992
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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Torsion-free Abelian Groups with Precobalanced Finite Rank Pure Subgroups

Abelian Groups, 2022
A. Giovannitti
semanticscholar   +1 more source