• NILPOTENCY OF IDEALS GENERATED BY SETS CONTAINED IN THE CENTER

Abstract

In this paper we consider R be a nonassociative and noncommutative ring. Let S be an additive subgroup of R such that (S, R) = 0. Now we take V={xÎR/ (x, y) = 0, for all yÎR}. From (S, R)=0, it follows that sÎV, where s is in S, and V is subring of R. Using these we show that V equals the center C of R, the set I=S+SR is an ideal of R and          (S+SR)ⁿ = Sⁿ+SⁿR for all positive integers n. Also it is proved that the ideal of R generated by S is nilpotent if and only if the subring generated by S is nilpotent.