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On Units in Near rings Let R be a near-ring with 1. In this paper, we show that multiplicative inverse of a unit (if it exists in R) in a commutative near-ring R with unity is unique. Further, if U is the collection of all units in a near-ring (R, +, .) with unity, then (U, .) is a group which implies that (U, +, .) is a near-field. In the end, we show that above mentioned results are also true for distributively generated near-ring (R, S) with unity. Date received: March 14, 2007 Copyright © 2007 by the author(s).
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Document # caul-51.
Distributively Generated Near rings
by
Sarwar J. Abbasi
Department of Mathematics, University of Karachi, Karachi, Pakistan
Coauthors: Kahkashan Iqbal,Faculty Member,College of Humanities & Sciences,PAF-KIET,Main Campus, Korangi Creek Base, Karachi, Pakistan