Results 11 to 20 of about 222 (151)

Indecomposable decompositions of torsion-free abelian groups [PDF]

Journal of Algebra, 2018
An indecomposable decomposition of a torsion-free abelian group $G$ of rank $n$ is a decomposition $G=A_1\oplus\cdots\oplus A_t$ where $A_i$ is indecomposable of rank $r_i$ so that $\sum_i r_i=n$ is a partition of $n$. The group $G$ may have decompositions that result in different partitions of $n$.
Adolf Mader, Phill Schultz
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Structure of Finite-Dimensional Protori

Axioms, 2019
A Structure Theorem for Protori is derived for the category of finite-dimensional protori (compact connected abelian groups), which details the interplay between the properties of density, discreteness, torsion, and divisibility within a finite ...
Wayne Lewis
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A Note on Additive Groups of Some Specific Torsion-Free Rings of Rank Three and Mixed Associative Rings

Discussiones Mathematicae - General Algebra and Applications, 2017
It is studied how rank two pure subgroups of a torsion-free Abelian group of rank three influences its structure and type set. In particular, the criterion for such a subgroup B to be a direct summand of a torsion-free Abelian group of rank three with ...
Najafizadeh Alireza, Woronowicz Mateusz
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A Note on the Square Subgroups of Decomposable Torsion-Free Abelian Groups of Rank Three

Annales Mathematicae Silesianae, 2018
A hypothesis stated in [16] is confirmed for the case of associative rings. The answers to some questions posed in the mentioned paper are also given. The square subgroup of a completely decomposable torsion-free abelian group is described (in both cases
Woronowicz Mateusz
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Characterization of the automorphisms having the lifting property in the category of abelian p-groups

International Journal of Mathematics and Mathematical Sciences, 2003
Let p be a prime. It is shown that an automorphism α of an abelian p-group A lifts to any abelian p-group of which A is a homomorphic image if and only if α=π idA, with π an invertible p-adic integer.
S. Abdelalim, H. Essannouni
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Rings on Abelian torsion-free groups of finite rank [PDF]

Beiträge zur Algebra und Geometrie / Contributions to Algebra and Geometry, 2021
In the class of reduced Abelian torsion-free groups $G$ of finite rank, we describe TI-groups, this means that every associative ring on $G$ is filial. If every associative multiplication on $G$ is the zero multiplication, then $G$ is called a $nil_a$-group.
E. I. Kompantseva, A. A. Tuganbaev
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Degrees of orders on torsion-free Abelian groups

Annals of Pure and Applied Logic, 2013
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Asher M. Kach, Karen M. Lange, Reed Solomon   +2 more
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Jump degrees of torsion-free abelian groups [PDF]

The Journal of Symbolic Logic, 2012
AbstractWe show, for each computable ordinal α and degree a > 0(α), the existence of a torsion-free abelian group with proper αth jump degree a.
Brooke M. Andersen, Asher M. Kach, Alexander G. Melnikov, Reed Solomon   +3 more
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On torsion-free abelian groups and Lie algebras [PDF]

Proceedings of the American Mathematical Society, 1958
It is known that many of the classes of simple Lie algebras of prime characteristic of nonclassical type have simple infinite-dimensional analogues of characteristic zero (see, for example, [4, p. 518]). We consider here analogues of those algebras which are defined by a modification of the definition of a group algebra.
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Spectral Analysis Implies Spectral Synthesis

Mathematics
In this paper we show that spectral analysis implies spectral synthesis for arbitrary varieties on locally compact Abelian groups that have no discrete subgroups of an infinite torsion-free rank.
László Székelyhidi
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