Results 21 to 30 of about 33,430 (215)
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
openaire +3 more sources
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
doaj +1 more source
$L^2$-Betti numbers and non-unitarizable groups without free subgroups [PDF]
, 2009 We show that there exist non-unitarizable groups without non-abelian free subgroups. Both torsion and torsion free examples are constructed. As a by-product, we show that there exist finitely generated torsion groups with non-vanishing first $L^2$-Betti ...
Osin, D.
core +1 more source
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
core +1 more source
Separable torsion-free abelian E∗-groups
Journal of Pure and Applied Algebra, 1998 The first half of this paper characterizes the torsion-free separable abelian groups \(G\) whose endomorphism semigroup \(E(G)^*\) admits a unique addition; that is, the endomorphism ring \(E(G)\) is isomorphic to any ring \(S\) for which \(E(G)^*\) is isomorphic to \(S^*\).
Lubimcev, O. +2 more
openaire +1 more source
On Weakly Transitive Torsion-Free Abelian Groups
Journal of Mathematical Sciences, 2021 This short note adds new information on a previous paper with the same subject by \textit{B. Goldsmith} and \textit{L. Strüngmann} [Commun. Algebra 33, No. 4, 1177--1191 (2005; Zbl 1142.20032)]. The results are: Proposition 2. If \(A\) is a reduced torsion-free group with strongly indecomposable pure subgroups and the set \(T(A)\) of types of all its ...
openaire +3 more sources
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
openaire +4 more sources
Torsion-free abelian groups are Borel complete
Annals of Mathematics, 2018 We prove that the Borel space of torsion-free Abelian groups with domain $ω$ is Borel complete, i.e., the isomorphism relation on this Borel space is as complicated as possible, as an isomorphism relation. This solves a long-standing open problem in descriptive set theory, which dates back to the seminal paper on Borel reducibility of Friedman and ...
Paolini G., Shelah S.
openaire +4 more sources
Finitely generated abelian groups of units [PDF]
, 2019 In 1960 Fuchs posed the problem of characterizing the groups which are the groups of units of commutative rings. In the following years, some partial answers have been given to this question in particular cases.
Del Corso, Ilaria
core +2 more sources
Characterizing group C*-algebras through their unitary groups: the Abelian case [PDF]
, 2010 We study to what extent group C*-algebras are characterized by their unitary groups. A complete characterization of which Abelian group C*-algebras have isomorphic unitary groups is obtained. We compare these results with other unitary-related invariants
Galindo, Jorge +1 more
core +1 more source