Results 201 to 210 of about 5,618 (233)

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.
exaly   +2 more sources

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.
exaly   +3 more sources

Direct Decomposition Theory of Torsion-Free Abelian Groups of Finite Rank: Graph Method

Lobachevskii Journal of Mathematics, 2018
E. Blagoveshchenskaya, D. Kunetz
exaly   +3 more sources

A Class of Torsion‐Free Abelian Groups of Finite Rank

Proceedings of the London Mathematical Society, 1965
M. C. R. Butler
semanticscholar   +3 more sources

Torsion-free Abelian groups of finite rank as endomorphic modules over their endomorphism ring

Mathematical Notes, 2013
D S Chistyakov, Chistyakov D S
exaly   +2 more sources

Balanced projective and cobalanced injective torsion free groups of finite rank

Acta Mathematica Hungarica, 1985
C Vinsonhaler
exaly   +2 more sources

Invariants and duality in some classes of torsion-free abelian groups of finite rank

Algebra and Logic, 1987
A A Fomin
exaly   +2 more sources

Endomorphism rings of torsion-free abelian groups of finite rank

Advances in Algebra and Model Theory, 2019
O. Mutzbauer
semanticscholar   +2 more sources

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.
openaire   +3 more sources

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
openaire   +2 more sources