International Journal of Mathematics and Mathematical Sciences
Volume 27 (2001), Issue 12, Pages 749-757
doi:10.1155/S0161171201006627

On Q-algebras

Joseph Neggers1 , Sun Shin Ahn2 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

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.