Results 151 to 160 of about 1,010 (185)

On locally free Abelian groups

Mathematical Notes, 2005
An Abelian group is called `locally free' if all its subgroups of finite rank are free. In the present paper it is proved that a torsion-free group is a locally free group if and only if it is a direct limit of an inductive system of finitely generated free groups such that each map in this system is an embedding onto a direct summand (such a system is
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On Torsion-Free Abelian k-Groups

Proceedings of the American Mathematical Society, 1987
A height sequence s is a function on primes p with values \(s_ p\) natural numbers or \(\infty\). The height sequence \(| x|\) of an element x in a torsion-free abelian group G is defined by \(| x|_ p=height\) of x at p. For a height sequence s, \(G(s)=\{x\in G:| x| \geq s\}\), \(G(ps)=\{x\in G(s):| x|_ p\geq s_ p+1\}\), \(G(s^*)=\{x\in G(s):\sum_{p}(|
Dugas, Manfred, Rangaswamy, K. M.
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ENDOPRIMAL TORSION-FREE SEPARABLE ABELIAN GROUPS

Journal of Algebra and Its Applications, 2004
We give a characterization for the groups in the title in terms of the graph structure of the critical types occurring in the group. Moreover, we give an example of arbitrarily large endoprimal indecomposable groups.
Göbel, R., Kaarli, K., Márki, L., Wallutis, S. L.   +3 more
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FREE ABELIAN TOPOLOGICAL GROUPS ON SPHERES

The Quarterly Journal of Mathematics, 1984
If X is a completely regular topological space, then the abelian topological group F(X) is a (Markov) free abelian topological group on X if X is a subspace of F(X), X generates F(X) algebraically and for every continuous mapping \(\phi\) of X into any abelian topological group G there exists a continuous homomorphism \(\Phi\) of F(X) into G that ...
Katz, Eli, Morris, Sidney A., Nickolas, Peter   +2 more
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Local Abelian Torsion-Free Groups

Journal of Mathematical Sciences, 2014
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Isomorphic Group Rings of Free Abelian Groups

Canadian Journal of Mathematics, 1982
S. K. Sehgal ([9], Problem 26) proposed the following question : Let A, B be rings and X an infinite cyclic group. Does AX ⋍ BX imply A ⋍ B? M. M. Parmenter and S. K. Sehgal (cf. [9], Chapter 4) proved that, under some strong assumptions concerning rings A, B, the answer is affirmative.
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Sum-free sets in abelian groups

Israel Journal of Mathematics, 2001
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Lev, Vsevolod, Łuczak, Tomasz, Schoen, Tomasz   +2 more
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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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Free subgroups of free abelian topological groups

Mathematical Proceedings of the Cambridge Philosophical Society, 1986
In this paper we prove a theorem which gives general conditions under which the free abelian topological group F(Y) on a space Y can be embedded in the free abeian topological group F(X) on a space X.
Katz, E., Morris, S. A., Nickolas, P.
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