International Journal of Mathematics and Mathematical Sciences
Volume 2013 (2013), Article ID 238490, 6 pages
http://dx.doi.org/10.1155/2013/238490
Research Article

On Symmetric Left Bi-Derivations in BCI-Algebras

G. Muhiuddin,1 Abdullah M. Al-roqi,1 Young Bae Jun,2 and Yilmaz Ceven3

1Department of Mathematics, University of Tabuk, Tabuk 71491, Saudi Arabia
2Department of Mathematics Education (and RINS), Gyeongsang National University, Jinju 660-701, Republic of Korea
3Department of Mathematics, Faculty of Science, Suleyman Demirel University, 32260 Isparta, Turkey

Received 15 February 2013; Accepted 30 May 2013

Academic Editor: Aloys Krieg

Copyright © 2013 G. Muhiuddin et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

The notion of symmetric left bi-derivation of a BCI-algebra X is introduced, and related properties are investigated. Some results on componentwise regular and d-regular symmetric left bi-derivations are obtained. Finally, characterizations of a p-semisimple BCI-algebra are explored, and it is proved that, in a p-semisimple BCI-algebra, F is a symmetric left bi-derivation if and only if it is a symmetric bi-derivation.