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Additive groups of rings whose subrings are ideals

Published online by Cambridge University Press:  17 April 2009

Shalom Feigelstock
Shalom Feigelstock
Affiliation:
Department of Mathematics and Computer Science, Bar Ilan University, Ramat-GanIsrael
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An Abelian group G is called an SI-group if for every ring R with additive group R+ = G, every subring S of R is an ideal in R. A complete description is given of the torsion SI-groups, and the completely decomposable torsion free SI-groups. Results are obtained in other cases as well.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 55 , Issue 3 , June 1997 , pp. 477 - 481
Copyright
Copyright © Australian Mathematical Society 1997

References

[1]Feigelstock, S., Additive groups of rings, Research Notes in Mathematics 8 (Pitman, London, 1983).Google Scholar
[2]Feigelstock, S., Additive groups of rings II, Research Notes in Mathematics 169 (Longman, Harlow, 1988).Google Scholar
[3]Fuchs, L., Infinite Abelian groups 1 (Academic Press, New York, London, 1971).Google Scholar
[4]Fuchs, L., Infinite Abelian groups 2 (Academic Press, New York, London, 1973).Google Scholar