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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

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