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Generalized near-fields

Published online by Cambridge University Press:  20 January 2009

C. V. L. N. Murty
C. V. L. N. Murty
Affiliation:
Department of MathematicsNagarjuna UniversityNagarjunanagar-522 510A.P.India
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By analogy with the concept of “inverse semi-group” in semi-group theory, in this paper we introduce the concept of “generalized near-field” in near-rings. A near-ring N is called a generalized near-field (GNF) if for each a ε N there exists a unique b ε N such that a = aba and b = bab, that is (N, ·) is an inverse semi-group. Surprisingly, this concept in rings coincides with that of “strong regularity”. But this is not true in the case of near-rings. Every GNF is strongly regular, but in general the converse is not true.

Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 27 , Issue 1 , February 1984 , pp. 21 - 24
Copyright
Copyright © Edinburgh Mathematical Society 1984

References

REFERENCES

1.Beidleman, J. C., A note on regular near-rings, J. Indian Math. Soc. 33 (1969), 207–210.Google Scholar
2.Howie, J. M., An Introduction to Semigroup Theory (Academic Press, New York, 1976).Google Scholar
3.Johnson, M. J., Radicals of regular near-rings, Monatsh. Math. 80 (1975), 331–341.CrossRefGoogle Scholar
4.Ligh, S., On division near-rings, Canad. J. Math. 21 (1969), 1366–1371.CrossRefGoogle Scholar
5.Ligh, S., On regular near-rings, Math. Japon. 15 (1970), 7–13.Google Scholar
6.Mason, G., Strongly regular near-rings, Proc. Edinburgh Math. Soc. 23 (1980), 27–35.CrossRefGoogle Scholar
7.Murty, C. V. L. N., Structure and ideal theory of strongly regular near-rings, Communicated to Proc. London Math. Soc. (1982).Google Scholar
8.Murty, C. V. L. N., On strongly regular near-rings II, Communicated to the International Symposium, New Delhi (1982).Google Scholar
9.Pilz, G., Near-rings (North-Holland, Amsterdam, 1977).Google Scholar
10.Raphael, R., Some remarks on regular and strongly regular rings, Canad. Math. Bull. 17 (1975), 709–712.CrossRefGoogle Scholar