Results 11 to 20 of about 22,610 (167)

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
  +9 more sources

A Cancellation Criterion for Finite-Rank Torsion-Free Abelian Groups [PDF]

Proceedings of the American Mathematical Society, 1985
In this paper, a necessary ring-theoretical criterion is given for a finite-rank torsion-free abelian group to have the cancellation property. This generalizes results obtained by L. Fuchs and F. Loonstra [5] for the rank-one case and resolves the cancellation problem for strongly indecomposable groups.
J. Stelzer
openaire   +3 more sources

Strongly Homogeneous Torsion Free Abelian Groups of Finite Rank [PDF]

Proceedings of the American Mathematical Society, 1976
An abelian group is strongly homogeneous if for any two pure rank 1 subgroups there is an automorphism sending one onto the other. Finite rank torsion free strongly homogeneous groups are characterized as the tensor product of certain subrings of algebraic number fields with finite direct sums of isomorphic subgroups of Q Q , the ...
Donald M. Arnold
  +4 more sources

The classification problem for torsion-free abelian groups of finite rank [PDF]

Journal of the American Mathematical Society, 2002
We prove that for each n ≥ 1 n \geq 1 , the classification problem for torsion-free abelian groups of rank n + 1 n+1 is not Borel reducible to that for torsion-free abelian groups of rank n n .
Simon Thomas
openaire   +3 more sources

Abelian rank of normal torsion-free finite index subgroups of polyhedral groups [PDF]

Transactions of the American Mathematical Society, 1985
Suppose that P P is a convex polyhedron in the hyperbolic 3 3 -space with finite volume and P P has integer ( > 1 ) ( > 1) submultiples of π \pi as dihedral angles.
Youn W. Lee
  +5 more sources

Isomorphism of modular group algebras of finite torsion-free rank coproducts of p-mixed countable abelian groups

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   +1 more source

A note on quasi-isomorphism of torsion free abelian groups of finite rank [PDF]

Czechoslovak Mathematical Journal, 1965
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Ladislav Procházka
openaire   +3 more sources

Finite rank torsion-free abelian groups uniserial over their endomorphism rings [PDF]

Proceedings of the American Mathematical Society, 1985
An abelian group is E E -uniserial if its lattice of fully invariant subgroups is totally ordered. Finite rank torsion-free reduced E E -uniserial groups are characterized. Such a group is a free module over the center C C of its endomorphism ring, and C C is a strongly ...
Jutta Hausen
  +5 more sources

Torsion-free Extensions of Torsion-free Abelian Groups of Finite Rank

, 2009
Duisburg, Essen, Univ., Diss ...
Stefan Friedenberg
openaire   +4 more sources

TORSION-FREE ABELIAN GROUPS OF FINITE RANK AND FIELDS OF FINITE TRANSCENDENCE DEGREE [PDF]

The Journal of Symbolic Logic
Abstract 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, JULIA FRANDSEN KNIGHT, RUSSELL GEDDES MILLER   +2 more
openaire   +3 more sources