(–1, 1) Rings without Nilpotent Elements
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DOI:
https://doi.org/10.14419/ijet.v7i4.10.20943Keywords:
Nonassociative ring, (–1, 1) ring, simple ring, idempotent, nilpotent.Abstract
A ring of type , was introduced by Albert and Kokoris [1,3] where in they have shown that a simple ring of type is either associative or contains no idempotent other than 1. In this paper we obtain further results on the residual cases, to prove that a nonassociative (-1,1) rings satisfying (x, x, y)2 = 0, for all elements of the rings imply (x, x, y) = 0. But then indeed (-1,1) rings which have no nilpotent elements are associative and there by all such rings are division rings.
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