Journal of Applied Mathematics
Volume 2012 (2012), Article ID 141684, 10 pages
http://dx.doi.org/10.1155/2012/141684
Research Article

Some Aspects of -Units in BCK-Algebras

Hee Sik Kim,1 J. Neggers,2 and Keum Sook So3

1Department of Mathematics, Hanyang University, Seoul 133-791, Republic of Korea
2Department of Mathematics, University of Alabama, Tuscaloosa, AL 35487-0350, USA
3Department of Mathematics, Hallym University, Chuncheon 200-702, Republic of Korea

Received 13 August 2012; Revised 2 November 2012; Accepted 9 November 2012

Academic Editor: Frank Werner

Copyright © 2012 Hee Sik Kim 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

We explore properties of the set of d-units of a -algebra. A property of interest in the study of -units in -algebras is the weak associative property. It is noted that many other -algebras, especially -algebras, are in fact weakly associative. The existence of -algebras which are not weakly associative is demonstrated. Moreover, the notions of a -integral domain and a left-injectivity are discussed.