Semi Nilpotent Elements

Authors

  • Kurdistan M. Ali Salahaddin University, College of Science, Department of Mathematics
  • Parween A. Hummadi Salahaddin University, College of Education, Department of Mathematics

DOI:

https://doi.org/10.23918/eajse.v3i2p241

Keywords:

Nilpotent, Semi Nilpotent

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.

References

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

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Published

2017-12-01

Issue

Vol. 3 No. 2 (2017)

Section

Articles

License

Creative Commons License

This work is licensed under a Creative Commons Attribution 4.0 International License.

Creative Commons License

Eurasian J. Sci. Eng is distributed under the terms of the Creative Commons Attribution License 4.0 (CC BY-4.0) https://creativecommons.org/licenses/by/4.0/

How to Cite

Ali, K. M., & Hummadi, P. A. (2017). Semi Nilpotent Elements. EURASIAN JOURNAL OF SCIENCE AND ENGINEERING, 3(2), 241-246. https://doi.org/10.23918/eajse.v3i2p241