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Certain conditions under which near-rings are rings

Published online by Cambridge University Press:  17 April 2009

Murtaza A. Quadri ,
M. Ashraf  and
Asma Ali
Murtaza A. Quadri
Affiliation:
Department of Mathematics Aligarh, Muslim University Aligarh, 202002, India
M. Ashraf
Affiliation:
Department of Mathematics Aligarh, Muslim University Aligarh, 202002, India
Asma Ali
Affiliation:
Department of Mathematics Aligarh, Muslim University Aligarh, 202002, India
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Abstract

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In 1969, Ligh proved that distributively generated (d-g) Boolean near-rings are rings, and hinted that some of the more complicated polynomial identities implying commutativity in rings may turn d-g near-rings into rings. In the present paper we investigate the following conditions: (1) xy = (xy)n(x, y); (2) xy = (yz)n (xy); (3) xy = ym (x, y)xn (x, y); (4) xy = xy n(x, y)x; (5) xy = xn(x, y)ym (x, y); finally prove that under appropriate additional hypotheses a d-g near-ring must be a commutative ring. Indeed the theorem proved here is a wide generalisation of many recently established results.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 42 , Issue 1 , August 1990 , pp. 91 - 94
Copyright
Copyright © Australian Mathematical Society 1990

References

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