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On extensions of nilpotent torsion rings by semisimple rings

Published online by Cambridge University Press:  17 April 2009

Ismail A. Amin  and
Ferenc A. Szász
Ismail A. Amin
Affiliation:
Department of Mathematics, Faculty of Science, Cairo University, Giza, Egypt.
Ferenc A. Szász
Affiliation:
Mathematical Institute, Hungarian Academy of Sciences, Budapest, Hungary.
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Abstract

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A class of rings in which each member is the extension of a nilpotent torsion ring by a semisimple semiartinian ring is presented.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 24 , Issue 1 , August 1981 , pp. 149 - 152
Copyright
Copyright © Australian Mathematical Society 1981

References

[1]Faith, Carl, Algebra II: ring theory (Die Grundlehren der mathematischen Wissenschaften, 191. Springer-Verlag, Berlin, Heidelberg, New York, 1976).Google Scholar
[2]Golan, Jonathan S., Localization of noncommutative rings (Pure and Applied Mathematics, 30. Marcel Dekker, New York, 1975).Google Scholar
[3]Golan, Jonathan S., Decomposition and dimension in module categories (Lecture Notes in Pure and Applied Mathematics, 33. Marcel Dekker, New York, Basel, 1977).Google Scholar
[4]Goldman, Oscar, “Rings and modules of quotients”, J. Algebra 13 (1969), 10–47.CrossRefGoogle Scholar
[5]Goldman, Oscar, “Elements of noncommutative arithmetic I”, J. Algebra 35 (1975), 308–341.CrossRefGoogle Scholar
[6]Jacobson, Nathan, Structure of rings, revised edition (American Mathematical Society Colloquium Publication, 37. American Mathematical Society, Providence, Rhode Island, 1964).Google Scholar
[7]Kertész, Andor, Vorlesungen Über artinsche Ringe (Akadémiai Kiadó, Budapest, 1968).Google Scholar
[8]Kertész, A., “Noethersche Ringe, die artinsch sind”, Acta Sci. Math. (Szeged) 31 (1970), 219–221.Google Scholar
[9]Stenström, Bo, Rings of quotients. An introduction to methods of ring theory (Die Grundlehren der mathematischen Wissenschaften, 217. Springer-Verlag, Berlin, Heidelberg, New York, 1975).Google Scholar
[10]Szász, F., “Über Ringe mit Minimalbedingung für Hauptrechtsideale. I”, Publ. Math. Debrecen 7 (1960), 54–64.CrossRefGoogle Scholar
[11]Szász, F., “Über Ringe mit Minimalbedingung für Hauptrechtsideale. II”, Acta Math. Acad. Sci. Hungar. 12 (1961), 417–439.CrossRefGoogle Scholar
[12]Szász, F., “Über Ringe mit Minimalbedingung für Hauptrechtsideale. III”, Acta Math. Acad. Sci. Hungar. 14 (1963), 447–461.CrossRefGoogle Scholar
[13]Szász, Ferenc, Radikale der Ringe (VEB Deutscher Verlag der Wissenschaften, Berlin, 1975).Google Scholar