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Groups Admitting only Finitely Many Nilpotent Ring Structures

Published online by Cambridge University Press:  20 November 2018

Shalom Feigelstock
Shalom Feigelstock*
Affiliation:
Bar-Ilan University, Ramat-Gaz, Israel
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Abstract

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The abelian groups which are the additive groups of only finitely many non-isomorphic (associative) nilpotent rings are studied. Progress is made toward a complete classification of these groups. In the torsion free case, the actual number of non-isomorphic nilpotent rings these groups support is obtained.

Keywords

20K99
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 29 , Issue 2 , 01 June 1986 , pp. 197 - 203
Copyright
Copyright © Canadian Mathematical Society 1986

References

1. Beaumont, R.A. and Wisner, R.J., Rings with additive group which is a torsion free group of rank two, Acta Sci. Math. Szeged, 20 (1959), pp. 105–116.Google Scholar
2. Borho, W., Uber die abelschen Gruppen aufdenen sich nur endliche vie le wesentlich verschiedene Ringe definieren lassen, Abh. Math. Sem. Univ. Hamburg, 37 (1972), pp. 98–107.Google Scholar
3. Feigelstock, S., Additive Groups of Rings, Research Notes in Mathematics, 83, (Pitman, Boston-London, 1983).Google Scholar
4. Fuchs, L., On quasi-nil groups, Acta Sci. Math. Szeged, 18 (1957), pp. 33–43.Google Scholar
5. Fuchs, L., Infinite Abelian Groups, 1 (1971); 2 (1973), (Academic Press, New York-London).Google Scholar
6. Kruse, R.L. and Price, D.T., Nilpotent Rings, (Gordon and Breach, New York-London, 1969).Google Scholar
7. Szele, T., Gruppentheoretische Beziehungen bei gewissen Ringkonstruktionen, Math. Z., 54 (1951), pp. 168–180.Google Scholar