Results 1 to 10 of about 24,182 (180)

Rings on Abelian Torsion-Free Groups of Finite Rank [PDF]

Beiträge zur Algebra und Geometrie / Contributions to Algebra and Geometry, 2021
This paper will be published in Beitr\"{a}ge zur Algebra und Geometrie / Contributions to Algebra and ...
Е. И. Компанцева, A. A. Tuganbaev   +1 more
semanticscholar   +7 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
semanticscholar   +4 more sources

Torsion-Free Abelian Groups of Finite Rank with Marked Bases [PDF]

Journal of Mathematical Sciences, 2021
We define a one-to-one correspondence between torsion-free Abelian groups of finite rank with marked bases and finite sequences of elements of finitely presented modules over the ring of polyadic numbers. This correspondence is a duality of two categories.
A. A. Fomin
semanticscholar   +4 more sources

Multiplication Groups of Abelian Torsion-Free Groups of Finite Rank [PDF]

Mediterranean Journal of Mathematics, 2023
For an Abelian group $G$, any homomorphism $μ\colon G\otimes G\rightarrow G$ is called a \textsf{multiplication} on $G$. The set $\text{Mult}\,G$ of all multiplications on an Abelian group $G$ itself is an Abelian group with respect to addition; the group is called the \textsf{multiplication group} of $G$.
Е. И. Компанцева, A. A. Tuganbaev   +1 more
semanticscholar   +4 more sources

Hypertypes of torsion-free abelian groups of finite rank [PDF]

Bulletin of the Australian Mathematical Society, 1989
Let G be a torsion-free abelian group of finite rank n and let F be a full free subgroup of G. Then G/F is isomorphic to T1 ⊕ … ⊕ Tn, where T1 ⊆ T2 ⊆ … ⊆ Tn ⊆ ℚ/ℤ. It is well known that type T1 = inner type G and type Tn = outer type G. In this note we give two characterisations of type Ti for 1 < i < n.
H. Pat Goeters, C. Vinsonhaler, W. Wickless   +2 more
semanticscholar   +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
semanticscholar   +5 more sources

A Note on Torsion-Free Abelian Groups of Finite Rank [PDF]

Proceedings of the American Mathematical Society, 1973
Let G be a torsion-free abelian group of rank n and X= {xl, *. , x,j a maximal set of rationally independent elements in G. It is well known that any g e G can be uniquely written g= oc1xl?+ +x, for some cci, . , ?C72, E Q, the rational numbers. This enables us to define, for any such (G, X), a collection of subgroups of Q and "natural" isomorphisms ...
W. Wickless, C. Vinsonhaler
semanticscholar   +5 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.
Adolf Mader, Phill Schultz
semanticscholar   +9 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 Ho, Julia F. Knight, Russell Miller   +2 more
semanticscholar   +5 more sources

Summands of finite rank torsion free abelian groups

Journal of Algebra, 1974
AbstractA finite rank torsion free abelian group has, up to isomorphism, only finitely many summands.
E.L Lady
semanticscholar   +4 more sources