Semi Nilpotent Elements

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 ZnG is semi nilpotent. It is shown that if p is prime and p divides the order of G, then ZpG has nontrivial semi nilpotent. Also it is proved that if G is a cyclic group of order qn, then every element of ZpG, p is prime, is semi nilpotent.

Keywords

• Nilpotent
• Semi Nilpotent