International Journal of Mathematics and Mathematical Sciences
Volume 25 (2001), Issue 3, Pages 205-211

On some classes of BCH-algebras

Muhammad Anwar Chaudhry1 and Hafiz Fakhar-Ud-Din2

1Department of Mathematical Sciences, King Fahd University of Petroleum and Minerals, Dhahran 31261, Saudi Arabia
2Department of Mathematics, Islamia University, Bahawalapur, Pakistan

Received 22 September 1999

Copyright © 2001 Muhammad Anwar Chaudhry and Hafiz Fakhar-Ud-Din. 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.


The concept of a BCH-algebra is a generalization of the concept of a BCI-algebra. It is shown that weakly commutative BCH-algebras are weakly commutative BCI-algebras. Moreover, the concepts of weakly positive implicative and weakly implicative BCH-algebras are defined and it is shown that every weakly implicative BCH-algebra is a weakly positive implicative BCH-algebra. The weakly positive implicative BCH-algebras are characterized with the help of their self maps. Two open problems are posed.