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Some mixed Abelian groups as modules over the ring of pseudo-rational numbers. (English) Zbl 0947.20037
Eklof, Paul C. (ed.) et al., Abelian groups and modules. Proceedings of the international conference in Dublin, Ireland, August 10-14, 1998. Basel: Birkhäuser. Trends in Mathematics. 87-100 (1999).
The author associates to any characteristic \(\chi=(m_p)\), \(p\in P\), a subring \(R_\chi\) of the ring \(\prod\widehat Z_p/p^{m_p}\widehat Z_p\) generated by a direct sum and images of the rationals \(k/n\) in a similar product for \(p\) not dividing \(n\). Some relations between such rings are studied. Additive groups of \(R_\chi\)-modules are characterized; in particular for \(\chi_\infty=(\infty,\infty,\dots)\) the class of finitely generated \(R_{\chi_\infty}\)-torsion \(R_{\chi_\infty}\)-modules coincides with the class of self-small groups \(G\) with \(G/T(G)\) finite rank divisible.
For the entire collection see [Zbl 0921.00018].

20K21 Mixed groups