Additive Groups of Unequivocal Rings

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A ring R is unequivocal if for every radical S, either S(R) = 0 or S(R) = R. A complete classification of the additive groups of unequivocal rings, which are not reduced torsion free, is given. The almost completely decomposable torsion free groups which are additive groups of unequivocal rings are also described completely.

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