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Semisimple rings on completely decomposable Abelian groups. (English. Russian original) Zbl 1166.20048

J. Math. Sci., New York 154, No. 3, 324-332 (2008); translation from Fundam. Prikl. Mat. 13, No. 3, 69-80 (2007).
The author characterizes the countable completely decomposable Abelian groups which admit a semisimple ring multiplication. The characterization is in terms of the order relation of the types of the rank 1 direct summands and the number of summands of each type.

MSC:

20K20 Torsion-free groups, infinite rank
16D60 Simple and semisimple modules, primitive rings and ideals in associative algebras
20K25 Direct sums, direct products, etc. for abelian groups
20M25 Semigroup rings, multiplicative semigroups of rings
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