International Journal of Mathematics and Mathematical Sciences
Volume 27 (2001), Issue 12, Pages 749-757
doi:10.1155/S0161171201006627
On Q-algebras
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.
Abstract
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), e∈X, has a product of the form x∗y=x−y+e, where x,y∈X when X is a field with |x|≥3.