Results 1 to 10 of about 222 (151)

Torsion-free abelian groups are Borel complete

Annals of Mathematics
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 ...
Saharon Shelah
exaly   +3 more sources

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
exaly   +3 more sources

Solving logistic tasks by parallelizing algorithms of the theory of direct decompositions of torsion-free abelian groups [PDF]

E3S Web of Conferences, 2023
The paper considers the principles of parallelization at marshalling yards and determines their importance. There are presented the methods for direct decompositions of torsion-free Abelian groups of finite rank.
Blagoveshchenskaya E., Gruzdev N., Zuev D.   +2 more
doaj   +1 more source

On Undecidability of Finite Subsets Theory for Torsion Abelian Groups

Mathematics, 2022
Let M be a commutative cancellative monoid with an element of infinite order. The binary operation can be extended to all finite subsets of M by the pointwise definition. So, we can consider the theory of finite subsets of M.
Sergey Mikhailovich Dudakov
doaj   +1 more source

Regularity in torsion-free abelian groups [PDF]

Czechoslovak Mathematical Journal, 1992
Eine Untergruppe \(B\) einer torsionsfreien abelschen Gruppe \(A\) heißt regulär (kritisch regulär) falls \(t^ B(b) = t^ A(b)\) für alle \(b\in B\) (falls für alle Typen \(t\) gilt: \(B(t) \setminus B^*(t)_ * \subset A(t)\setminus A^*(t)_ *\)). Die Untergruppe \(B\) heißt stark regulär, falls \(B\) eine reguläre und eine kritisch reguläre Untergruppe ...
Müller, Edgar, Mutzbauer, Otto
openaire   +2 more sources

Torsion-free abelian groups revisited [PDF]

Rendiconti del Seminario Matematico della Università di Padova, 2020
Let G be a torsion-free abelian group of finite rank. The orbits of the action of Aut( G ) on the set of maximal independent subsets of
openaire   +2 more sources

A Distinguished Subgroup of Compact Abelian Groups

Axioms, 2022
Here “group” means additive abelian group. A compact group G contains δ–subgroups, that is, compact totally disconnected subgroups Δ such that G/Δ is a torus.
Dikran Dikranjan, Wayne Lewis, Peter Loth, Adolf Mader   +3 more
doaj   +1 more source

On Some Results of a Torsion-Free Abelian Kernel Group

Recoletos Multidisciplinary Research Journal, 2014
In [6], for any torsion-free abelian groups Gand H, the kernel of Hin GisfHGGHHomfker, ker,. The kernel of Hin Gis a pure fully invariant subgroup of G.
Ricky B. Villeta
doaj   +1 more source

On Some Results of a Torsion-Free Abelian Trace Group

Recoletos Multidisciplinary Research Journal, 2014
In [6], givenany torsion-free abelian groups Gand H, the pure trace of Hin Gis *,:,GHHomfHfGHtr which is equivalent to the set ZnGHHomfHfngGgsomefor ,,:.The pure trace GHtr, is a pure fully invariant subgroup of G.
Ricky B. Villeta
doaj   +1 more source

Invariants for a class of torsion-free abelian groups [PDF]

Proceedings of the American Mathematical Society, 1989
In this note we present a complete set of quasi-isomorphism invariants for strongly indecomposable abelian groups of the form G = G
Arnold, D., Vinsonhaler, C.
openaire   +2 more sources