Results 121 to 130 of about 240 (146)

A Class of Torsion-Free Abelian Groups of Finite Rank

Proceedings of the London Mathematical Society, 1965
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TORSION-FREE ABELIAN GROUPS WITH FINITE RANK ENDOMORPHISM RINGS

Quaestiones Mathematicae, 1991
H. Pat Goeters
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Endomorphism rings of torsion-free abelian groups of finite rank

, 2019
Otto Mutzbauer
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FINITE AUTOMORPHISM GROUPS OF TORSION-FREE ABELIAN GROUPS OF FINITE RANK

Mathematics of the USSR-Izvestiya, 1989
A well-known result of Jónsson states that each torsion-free group G of finite rank has a quasi-direct decomposition i.e. a subgroup A of finite index which is a direct sum of pure strongly indecomposable subgroups. For such a group several quasi-direct decompositions do exist all being quasi-isomorphic but generally not isomorphic.
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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
The paper deals with new specific constructions of indecomposable torsion-free abelian groups of rank two and nonzero rings on them. They illustrate purely theoretical results and complement quite rare examples obtained during the classical as well as recent research of additive groups of rings.
Andruszkiewicz, Ryszard R., Woronowicz, Mateusz   +1 more
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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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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.
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Torsion free Abelian groups of finite rank and their direct decompositions

Journal of Soviet Mathematics, 1991
In this note it is understood that all groups are torsion-free abelian groups of finite rank. The author reduces the problem of a description of the groups to the following questions: 1) Classification of strongly indecomposable groups; 2) Classification of categories \(\bar M^ p\); 3) Description of the kinds of groups; 4) Investigation of cones in ...
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On the Complexity of the Classification Problem for Torsion-Free Abelian Groups of Finite Rank

Bulletin of Symbolic Logic, 2001
In this paper, we shall discuss some recent contributions to the project [15, 14, 2, 18, 22, 23] of explaining why no satisfactory system of complete invariants has yet been found for the torsion-free abelian groups of finite rank n ≥ 2. Recall that, up to isomorphism, the torsion-free abelian groups of rank n are exactly the additive subgroups of the ...
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On the torsion-free ranks of finitely generated nilpotent groups and of their abelian subgroups

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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