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On strongly regular near-rings

Published online by Cambridge University Press:  20 January 2009

Y. V. Reddy  and
C. V. L. N. Murty
Y. V. Reddy
Affiliation:
Department of Mathematics, Nagarjuna UniversityNagarjunanagar- 522 510A.P.INDIA
C. V. L. N. Murty
Affiliation:
Department of Mathematics, Nagarjuna UniversityNagarjunanagar- 522 510A.P.INDIA
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According to Mason [1] a right near-ring N is called (i) left (right) strongly regular if for every a there is an x in N such that a = xa2 (a = a2x) and (ii) left (right) regular if for every a there is an x in N such that a = xa2 (a = a2x) and a = axa. He proved that for a zerosymmetric near-ring with identity, the notions of left regularity, right regularity and left strong regularity are equivalent. The aim of this note is to prove that these three notions are equivalent for arbitrary near-rings. We also show that if N satisfies dec on iV-subgroups, then all the above four notions are equivalent.

Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 27 , Issue 1 , February 1984 , pp. 61 - 64
Copyright
Copyright © Edinburgh Mathematical Society 1984

References

REFERENCES

1.Mason, G., Strongly regular near-rings, Proc. Edinburgh Math. Soc. 23 (1980), 27–35.CrossRefGoogle Scholar
2.Pilz, G., Near-rings (North-Holland, Amsterdam, 1977).Google Scholar