Results 181 to 190 of about 33,430 (215)

Torsion-free Abelian Groups, Valuations and Twisted Group Rings

Canadian Mathematical Bulletin, 1988
AbstractAnderson and Ohm have introduced valuations of monoid rings k[Γ] where k is a field and Γ a cancellative torsion-free commutative monoid. We study the residue class fields in question and solve a problem concerning the pure transcendence of the residue fields.
Bastos, Gervasio G., Viswanathan, T. M.
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Torsion-Free Abelian Groups

2000
There are two equivalence relations on torsion-free abelian groups that are weaker than group isomorphism, namely quasi-isomorphism and isomorphism at a prime p. Properties of these equivalence relations are conveniently expressed in a categorical setting.
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Strictly purely correct, torsion-free Abelian groups

Journal of Mathematical Sciences, 2008
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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On Torsion-Free Minimal Abelian Groups

Communications in Algebra, 2005
ABSTRACT An abelian group is said to be minimal if it is isomorphic to all its subgroups of finite index. In this article we show that torsion-free groups which are complete in their ℤ-adic topology or are of p-rank not greater than 1, for all primes p, are minimal.
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Strongly homogeneous torsion-free Abelian groups

Siberian Mathematical Journal, 1983
All groups in this paper are abelian. A torsion-free group G is called strongly homogeneous if for any rank 1 pure subgroups A and B of G there exists \(\alpha \in Aut G\) such that \(\alpha A=B\). An associative ring R with identity is called strongly homogeneous if every element of R is an integral multiple of a unit.
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Fully transitive torsion-free Abelian groups

Algebra and Logic, 1990
A torsion-free abelian group \(G\) is called fully transitive (transitive) if for any elements \(0\neq a\), \(b\in G\) with height sequences \(h^ G(a)\leq h^ G(b)\) \((h^ G(a)=h^ G(b))\) there exists an endomorphism (automorphism) \(\alpha\in\hbox{End}(G)\) \((\alpha\in \hbox{Aut} G)\) such that \(\alpha a=b\).
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Hierarchies of torsion-free Abelian groups

Algebra and Logic, 1986
Using the arithmetic hierarchy of sets one can define the arithmetic hierarchy of Abelian groups. Let N be the set of all natural numbers, and let X denote one of the symbols \(\Sigma^ 0_ n\), \(\Pi^ 0_ n\), \(\Delta^ 0_ n\), where \(n\geq 1\). A map \(\nu\) of the set N onto the Abelian group A is said to be an enumeration of this group. The pair (A,\(
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Enumerations and Completely Decomposable Torsion-Free Abelian Groups

Theory of Computing Systems, 2009
The main results of this paper are the following: For any family \(R\) of finite sets there exists a completely decomposable torsion-free abelian group \(G_{R}\) of infinite rank such that \(G_{R}\) has an \(X\)-computable copy if and only if \(R\) has a \(\Sigma_{2}^{X}\)-computable enumeration (Theorem 4).
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Enumerations and Torsion Free Abelian Groups

2007
We study possible spectrums of torsion free Abelian groups. We code families of finite sets into group and set up the correspondence between their algorithmic complexities.
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Projective classes of torsion free abelian groups. II

Acta Mathematica Hungarica, 1984
[Part I, cf. the author and \textit{C. Vinsonhaler}, ibid. 39, 195-215 (1982; Zbl 0496.20041).] Let \({\mathcal C}\) be the category of torsion free abelian groups of finite rank, \(G\in {\mathcal C}\), \(C_ 0(G)=\{A\in {\mathcal C}|\) G is projective with respect to all \({\mathcal C}\) exact sequences (pure exact sequences) of the form: \(0\to K\to A\
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