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Ideal extensions of Γ-rings

Part of: Generalizations

Published online by Cambridge University Press:  09 April 2009

A. J. M. Snyders  and
S. Veldsman
A. J. M. Snyders
Affiliation:
University of Port Elizabeth, P.O. Box 1600, Port Elizabeth (6000), Republic of South Africa
S. Veldsman
Affiliation:
University of Port Elizabeth, P.O. Box 1600, Port Elizabeth (6000), Republic of South Africa
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Abstract

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Given Γ-rings N1 and N2, a construction similar to the Everett sum of rings to find all possible extensions of N1 by N2 is given. Unlike the case of rings, it is not possible to find for any Γ-ring M an ideal extension that has a unity. Furthermore, contrary to the ring case, a Γ-ring with unity can not be characterized as a Γ-ring which is a direct summand in every extension thereof.

MSC classification

Secondary: 16Y99: None of the above, but in this section
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 54 , Issue 3 , June 1993 , pp. 368 - 392
Copyright
Copyright © Australian Mathematical Society 1993

References

[1]Barnes, W. E., ‘On the Γ-rings of Nobusawa’, Pacific J. Math. 18 (1966), 411–422.Google Scholar
[2]Booth, G. L. and Groenewald, N. J., ‘On uniformaly strongly prime gamma rings’, Bull. Austral. Math. Soc. 37 (1988), 437–445.Google Scholar
[3]Everett, C. J., ‘An extension theory for rings’, Amer. J. Math. 64 (1942), 363–370.CrossRefGoogle Scholar
[4]Kyuno, S., ‘A gamma ring with the right and left unities’, Math. Japon. 24 (1979), 191–193.Google Scholar
[5]Nobusawa, N., ‘On a generalization of the ring theory’, Osaka J. Math. 1 (1964), 81–89.Google Scholar
[6]Petrich, M., ‘Ideal extensions of rings’, Acta Math. Hungar. 45 (1985), 263–283.Google Scholar
[7]Rédei, L., Algebra, Volume 1 (Pergamon Press, Oxford, 1967).Google Scholar
[8]Schreier, O., ‘Über die Erweiterung von Gruppen’, Monatsh. Math. 34 (1926), 165–180.CrossRefGoogle Scholar