Results 111 to 120 of about 238 (157)

Torsion-free Abelian groups of finite rank without nilpotent endomorphisms

Siberian Mathematical Journal, 1988
See the review in Zbl 0645.20033.
S. F. Kozhukhov
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Torsion-free Abelian groups of finite rank as endomorphic modules over their endomorphism ring

Mathematical Notes, 2013
Let \(R\) be an associative ring with identity and let \(V\) and \(W\) be unitary left \(R\)-modules. A function \(f\colon V\to W\) is called homogeneous if \(f(rv)=rf(v)\) for all \(r\in R\) and \(v\in V\). The set of all such functions is denoted \(M_R(V,W)\) and we abbreviate \(M_R(V,V)\) as \(M_R(V)\).
D. S. Chistyakov
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On a class of torsion-free abelian groups of finite rank

Mathematical Notes, 1994
A class of torsion free finite rank Abelian groups is characterized in this paper. The class can be treated as a generalization of Murley's \(\mathcal E\)-group class. The results of \textit{A. Fomin}'s paper [Algebra Logika 26, No. 1, 63-83 (1987; Zbl 0638.20030)] are applied.
I. V. Karpova
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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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Duality in some classes of torsion-free Abelian groups of finite rank

Siberian Mathematical Journal, 1987
Let \(\sigma\), \(\tau\) be a pair of types of torsion-free (abelian) groups of rank 1 which are determined by characteristics \((k_ p)\), \((m_ p)\) such that \(k_ p\leq m_ p\) for all primes \(p\). A torsion-free group \(A\) of finite rank \(n\) belongs to the class \(D^{\tau}_{\sigma}\) iff there exists a free subgroup \(J\) of rank \(n\) of \(A ...
A. A. Fomin
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The Grothendieck Group of Torsion-Free Abelian Groups of Finite Rank

Proceedings of the London Mathematical Society, 1963
Joseph Rotman
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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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