Semi Nilpotent Elements

Authors: Kurdistan M. Ali1 & Parween A. Hummadi2
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 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

doi: 10.23918/eajse.v3i2p241

Download the PDF Document from here.

Burton, D. M. (1980). Elementary Number Theory. Allyn and Bacon.
Dummit, D. S., & Foote, R. M. (2004). Abstract Algebra (Vol.3). John Wiley and Sons, Inc.
Schroeder, M. R. (2006). Number theory in science and communication: with applications in
cryptography, physics, digital information, computing and self-similarity. Springer series in
information sciences.
Kandasamy, W. V. (1997). On semi nilpotent elements of a ring. Punjab Univ. J. Math, 30, 143-147.
Kandasamy, W. V. (2002). Smarandache Rings. American Research Press