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Mixed Abelian groups as modules over their endomorphism rings. (Russian. English summary) Zbl 1019.20023
Mixed Abelian groups \(A\) are studied as left modules over their endomorphism rings \(E(A)\). The main results are: (i) the torsion part \(T(A)\) is flat over \(E(A)\) iff each \(p\)-primary component of \(A\) is either bounded or admits an unbounded basic subgroup, (ii) if \(A\) is a pure subgroup of the direct product of its \(p\)-primary components then \(E(A)\)-flat [-projective] dimensions of \(A\) and \(A/T(A)\) are equal [if \(A\) is not \(E(A)\)-projective].

20K30 Automorphisms, homomorphisms, endomorphisms, etc. for abelian groups
20K40 Homological and categorical methods for abelian groups
20K21 Mixed groups
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