A note on additive groups of some specific associative rings
Abstract
Almost complete description of abelian groups (A,+, 0) such that every associative ring R with the additive group A satisfies the condition: every subgroup of A is an ideal of R, is given. Some new results for SR-groups in the case of associative rings are also achieved. The characterization of abelian torsion-free groups of rank one and their direct sums which are not nil-groups is complemented using only elementary methods.
Keywords
nil-groups; ideals; associative rings
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Instytut Matematyki, Uniwersytet w Białymstoku Poland
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