Results 11 to 20 of about 33,164 (164)

TORSION-FREE WEAKLY TRANSITIVE ABELIAN GROUPS

Communications in Algebra, 2005
ABSTRACT We introduce the notion of weak transitivity for torsion-free abelian groups. A torsion-free abelian group G is called weakly transitive if for any pair of elements x, y ∈ G and endomorphisms ϕ, ψ ∈ End(G) such that xϕ = y, yψ = x, there exists an automorphism of G mapping x onto y.
Goldsmith, Brendan, Strungmann, Lutz
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Localizations of torsion-free abelian groups

Journal of Algebra, 2004
The author considers the localizations of torsion-free Abelian groups, more precisely, the localizations of free groups, of cotorsion-free groups, and of finite rank Butler groups. For Abelian groups \(A,B\) a homomorphism \(\alpha\colon A\to B\) is said to be a `localization' of \(A\) if, for all \(f\colon A\to B\), there is a unique \(\varphi\colon B\
Manfred Dugas
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Localizations of torsion-free abelian groups II

Journal of Algebra, 2005
A homomorphism \(\alpha\colon A\to B\) between Abelian groups \(A,B\) is called a localization of \(A\) if every homomorphism \(\varphi\) from \(A\) to \(B\) has a unique extension to an endomorphism \(\psi\) of \(B\) in the sense that \(\varphi=\psi\circ\alpha\).
Manfred Dugas
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Nearly isomorphic torsion free abelian groups

Journal of Algebra, 1975
AbstractLet K be the Krull-Schmidt-Grothendieck group for the category of finite rank torsion free abelian groups. The torsion subgroup T of K is determined and it is proved that KT is free. The investigation of T leads to the concept of near isomorphism, a new equivalence relation for finite rank torsion free abelian groups which is stronger than ...
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Types in torsion free Abelian groups

Communications in Algebra
In this paper we study (logical) types and isotypical equivalence of torsion free Abelian groups. We describe all possible types of elements and standard 2-tuples of elements in these groups and classify separable torsion free Abelian groups up to isotypicity.
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Protoadditive functors, derived torsion theories and homology [PDF]

, 2011
Protoadditive functors are designed to replace additive functors in a non-abelian setting. Their properties are studied, in particular in relationship with torsion theories, Galois theory, homology and factorisation systems.
Everaert, Tomas, Gran, Marino
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Semi-localizations of semi-abelian categories [PDF]

, 2015
A semi-localization of a category is a full reflective subcategory with the property that the reflector is semi-left-exact. In this article we first determine an abstract characterization of the categories which are semi-localizations of an exact Mal ...
Gran, Marino, Lack, Stephen
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The group of endotrivial modules for the symmetric and alternating groups. [PDF]

, 2010
We complete a classification of the groups of endotrivial modules for the modular group algebras of symmetric groups and alternating groups. We show that, for n ≥ p2, the torsion subgroup of the group of endotrivial modules for the symmetric groups is ...
Carlson, Jon, Hemmer, Dave, Mazza, Nadia
core   +1 more source

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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