Semi Nilpotent Elements

Authors: Kurdistan M. Ali¹ & Parween A. Hummadi^2
1Salahaddin University, College of Science, Department of Mathematics
²Salahaddin University, College of Education, Department of Mathematics

Abstract: In this paper we study semi nilpotent elements in rings. It is shown that every element of Z _nwhere n is square free is a trivial semi nilpotent. It is proved that every nontrivial nilpotent element is a nontrivial semi nilpotent. Conditions are given under which every element of the group ring Z_nG is semi nilpotent. It is shown that if p is prime and p divides the order of G, then Z_pG has nontrivial semi nilpotent. Also it is proved that if G is a cyclic group of order qⁿ, then every element of Z_pG, p is prime, is semi nilpotent.

Keywords: Nilpotent, Semi Nilpotent

doi: 10.23918/eajse.v3i2p241

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