International Journal of Mathematics and Mathematical Sciences
Volume 27 (2001), Issue 12, Pages 749-757

On Q-algebras

Joseph Neggers,1 Sun Shin Ahn,2 and Hee Sik Kim3

1Department of Mathematics, University of Alabama, Tuscaloosa 35487-0350, AL, USA
2Department of Mathematics Education, Dongguk University, Seoul 100-715, Korea
3Department of Mathematics, Hanyang National University, Seoul 133-791, Korea

Received 29 January 2001

Copyright © 2001 Joseph Neggers 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.


We introduce a new notion, called a Q-algebra, which is a generalization of the idea of BCH/BCI/BCK-algebras and we generalize some theorems discussed in BCI-algebras. Moreover, we introduce the notion of “quadratic” Q-algebra, and show that every quadratic Q-algebra (X;,e), eX, has a product of the form xy=xy+e, where x,yX when X is a field with |x|3.