Results 11 to 20 of about 2,671 (177)
The classification problem for S-local torsion-free abelian groups of finite rank
Advances in Mathematics, 2011 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
S. Thomas
semanticscholar +4 more sources
A matrix description for torsion free abelian groups of finite rank
Rendiconti del Seminario Matematico della Università di Padova, 2020 We describe torsion free abelian groups of finite rank applying matrices with polyadic entries. This description can be considered as a modification of the classic description by A. I. Mal'cev.
A. Fomin
openaire +3 more sources
TORSION-FREE ABELIAN GROUPS OF FINITE RANK AND FIELDS OF FINITE TRANSCENDENCE DEGREE
The Journal of Symbolic LogicAbstract Let $\operatorname {TFAb}_r$ be the class of torsion-free abelian groups of rank r, and let $\operatorname {FD}_r$ be the class of fields of characteristic $0$ and transcendence degree r. We compare these classes using various notions.
MENG-CHE TURBO HO +2 more
openaire +3 more sources
Completely decomposable direct summands of torsion-free abelian groups of finite rank [PDF]
Proceedings of the American Mathematical Society, 2017 Let $A$ be a finite rank torsion--free abelian group. Then there exist direct decompositions $A=B\oplus C$ where $B$ is completely decomposable and $C$ has no rank 1 direct summand. In such a decomposition $B$ is unique up to isomorphism and $C$ unique up to near-isomorphism.
Mader, Adolf, Schultz, Phill
openaire +4 more sources
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
doaj +2 more sources
The classification of torsion-free abelian groups of finite rank up to isomorphism and up to quasi-isomorphism [PDF]
, 2009 The isomorphism and quasi-isomorphism relations on the $p$-local torsion-free abelian groups of rank $n\geq3$ are incomparable with respect to Borel reducibility.
Samuel Coskey
semanticscholar +2 more sources
Dualities for torsion-free abelian groups of finite rank
Journal of Algebra, 1990 All groups considered here are torsion-free abelian groups of finite rank. Let F be a full free subgroup of such a group G. The finite outer type of G, FOT(G), is \((...,\pi_ p,...)\), where \(p^{\pi_ p}\) is the order of a maximal cyclic summand in the p-component of the reduced part of G/F.
Vinsonhaler, C, Wickless, W
openaire +3 more sources
An equivalence relation for torsion-free abelian groups of finite rank
Journal of Algebra, 1992 The equivalence relation in question is defined as follows: let \({^\perp G}=\{X:\Hom(X,G)=0\}\). Then \(G\) is equivalent to \(H\) if and only if \({^\perp G}={^\perp H}\). Since this relation is coarser than quasi-isomorphism, it is useful in classifying torsion-free abelian groups.
W. Wickless
openaire +2 more sources
Le Matematiche, 2006 Suppose G is with finite torsion-free rank a coproduct of p-mixed countable abelian groups and F is a field with characteristic p such that the group algebras FG and FH are F -isomorphic for another group H . Then G and H are isomorphic.
Peter Danchev
doaj +2 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
A. V. Blazhenov
openaire +3 more sources