Results 131 to 140 of about 24,618 (173)

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 ...
S. Thomas
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Direct decompositions of torsion-free Abelian groups of finite rank

Journal of Soviet Mathematics, 1985
Translation from Zap. Nauchn. Semin. Leningr. Otd. Mat. Inst. Steklova 132, 17-25 (Russian) (1983; Zbl 0524.20029).
E. Blagoveshchenskaya
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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.
S. Kozhukhov
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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.
M. A. Turmanov
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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.
R. Grigutis
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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 ...
A. V. Yakovlev
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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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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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Torsion-free Abelian groups of finite rank without nilpotent endomorphisms

Siberian Mathematical Journal, 1988
See the review in Zbl 0645.20033.
S. Kozhukhov
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Categories of Mixed and Torsion-Free Finite Rank Abelian Groups

, 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.
A. A. Fomin, W. Wickless
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