A note on the square subgroups of decomposable torsion-free abelian groups of rank three
Abstract
A hypothesis stated in [16] is confirmed for the case of associative rings. The answers to some questions posed in the mentioned paper are also given. The square subgroup of a completely decomposable torsion-free abelian group is described (in both cases of associative and general rings). It is shown that for any such a group A, the quotient group modulo the square subgroup
of A is a nil-group. Some results listed in [16] are generalized and corrected. Moreover, it is proved that for a given abelian group A, the square subgroup of A considered in the class of associative rings, is a characteristic subgroup of A.
Keywords
torsion-free abelian groups; associative rings; square subgroups; types
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Instytut Matematyki, Uniwersytet w Białymstoku Poland
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