Results 11 to 20 of about 238 (157)

Multiplication Groups of Abelian Torsion-Free Groups of Finite Rank

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
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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
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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

On controllers of prime ideals in group algebras of torsion-free abelian groups of finite rank [PDF]

, 2003
In the presented paper we consider some methods of studying of prime ideals in group algebras of abelian groups of finite ...
A. V. Tushev
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Duality of the categories of torsion-free Abelian groups of finite rank and quotient divisible Abelian groups [PDF]

Journal of Mathematical Sciences, 2010
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
A. V. Yakovlev
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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.
C. Vinsonhaler, W. Wickless
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Torsion-free Extensions of Torsion-free Abelian Groups of Finite Rank

, 2009
Duisburg, Essen, Univ., Diss ...
Stefan Friedenberg
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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
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On the $p$-rank of torsion-free Abelian groups of finite rank [PDF]

Czechoslovak Mathematical Journal, 1962
Ladislav Procházka
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Endomorphism rings and subgroups of finite rank torsion-free Abelian groups [PDF]

Rocky Mountain Journal of Mathematics, 1982
Donald M. Arnold
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