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Griffith, P. , Infinite Abelian Group Theory , The University of Chicago Press (Chicago and London, 1970). Griffith P. Infinite Abelian Group Theory

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de Bruijn, N. G. , On the factorization of finite abelian groups, Indag. Math. Kon. Ned. Akad. Wetersch. , 15 (1953), 258–264. MR 15 ,8g Bruijn N. G. On the

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Arnold, D. , Finite Rank Torsion-Free Abelian Groups and Rings, Lecture Notes in Math. 931 , Springer-Verlag, New York, 1982. MR 84d :20002

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Abstract  

The non-trivial hereditary monocoreflective subcategories of the Abelian groups are the following ones: {G ∈ Ob Ab | G is a torsion group, and for all gG the exponent of any prime p in the prime factorization of o(g) is at most E(p)}, where E(·) is an arbitrary function from the prime numbers to {0, 1, 2, …,∞}. (o(·) means the order of an element, and n ≤ ∞ means n < ∞.) This result is dualized to the category of compact Hausdorff Abelian groups (the respective subcategories are {G ∈ Ob CompAb | G has a neighbourhood subbase {G α} at 0, consisting of open subgroups, such that G/G α is cyclic, of order like o(g) above}), and is generalized to categories of unitary R-modules for R an integral domain that is a principal ideal domain. For general rings R with 1, an analogous theorem holds, where the hereditary monocoreflective subcategories of unitary left R-modules are described with the help of filters L in the lattice of the left ideals of the ring R. These subcategories consist of those left R-modules, for which the annihilators of all elements belong to L. If R is commutative, then this correspondence between these subcategories and these filters L is bijective.

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Abstract  

This paper gives a complete description of the behaviour of torsion-free abelian groups of rank 3 with respect to endoprimality.

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Abstract  

Let G be a p-reduced Abelian group and R a commutative unital ring of prime characteristic p such that for each natural number i the subring

\documentclass{aastex} \usepackage{amsbsy} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{bm} \usepackage{mathrsfs} \usepackage{pifont} \usepackage{stmaryrd} \usepackage{textcomp} \usepackage{upgreek} \usepackage{portland,xspace} \usepackage{amsmath,amsxtra} \pagestyle{empty} \DeclareMathSizes{10}{9}{7}{6} \begin{document} $$R^{p^i }$$ \end{document}
has nilpotent elements. It is shown that if S(RG) is the normalized Sylow p-group in the group ring RG, then S(RG) is torsion-complete if and only if G is a bounded p-group. This strengthens our former results on this subject.

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Authors: P. J. Hilton and S. M. Yahya
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High extensions of Abelian groups

To professorL. Fuchs

Authors: D. K. Harrison, J. M. Irwin, C. L. Peercy and E. A. Walker
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