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The additive groups of subdirectly irreducible rings

Published online by Cambridge University Press:  17 April 2009

Shalom Feigelstock
Shalom Feigelstock
Affiliation:
Department of Mathematics, Bar-Ilan University, Ramat-Gan, Israel.
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Abstract

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An abelian group G is said to be subdirectly irreducible if there exists a subdirectly irreducible ring R with additive group G. If G is subdirectly irreducible, and if every ring R with additive group G, and R2 ≠ 0, is subdirectly irreducible, then G is said to be strongly subdirectly irreducible. The torsion, and torsion free, subdirectly irreducible and strongly subdirectly irreducible groups are classified completely. Results are also obtained concerning mixed subdirectly irreducible and strongly subdirectly irreducible groups.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 20 , Issue 2 , April 1979 , pp. 165 - 170
Copyright
Copyright © Australian Mathematical Society 1979

References

[1]Fuchs, László, Infinite abelian groups, Volume I (Pure and Applied Mathematics, 36. Academic Press, New York and London, 1970).Google Scholar
[2]Fuchs, László, Infinite abelian groups, Volume II (Pure and Applied Mathematics, 36–11. Academic Press, New York and London, 1973).Google Scholar