Strongly Semiunits and Tri-Regular Elements in Rings

Authors: Parween Ali Hummadi & Suham Hamad Awla

Abstract:  In this paper we study semiunit elements in the group ring Z2G, where G is a cyclic group and we introduce and discuss strongly semiunit elements in Zn, for n=p, 2p, p2 where p is an odd prime. We define and study tri-regular elements in Zn and in the group ring, Z2G where G is a cyclic group.

Keywords: Semiunit, Strongly Semiunit and Tri-Regular Element

Download the PDF Document from here.

doi: 10.23918/eajse. v4i2p141

References

Burton, D. (1980). Elementary number theory. Allyn and Bacon Inc.

Hummadi, P. (2009). S-units and S-idempotents. Zanco Journal of Pure and Applied Sciences, 21(4), 137-144.

Hummadi, P., &  Usman, S. (2010). Smarandache idempotents in certain type of

group rings. Journal of Sulaymania University, 13(1).

Hung, C., &  Guo, Y. (2010). On -idempotents. African Dispora Journal of Mathematics, 9(1), 64-67.

Hungerford, T. (1974).  Algebra. Springer-velag.

Muhammad, A. (2010). On Tripotents and Smarandache Triple Tripotents in Finite Rings  and Group Rings , Msc thesis, Salahaddin University College of Education.

Piacentini, C. (2009). Elementary number theory, cryptography and codes. VSpringer-Verlag Berlin Heidelberg.

Rosen, K. (2000). Elementary number theory and its applications. Addison-welsey Longman.

Vasantha, W. B., & Cherty, M. (2005). Smarandache idempotent in finite ring  and in group ring . Scientia Magna., 1(2), 179-187.

Vasantha, W. B. (2002).  Kandasamy, smarandache rings. American Research Press.