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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].

##### MSC:
 20K21 Mixed groups