International Journal of Mathematics and Mathematical Sciences
Volume 25 (2001), Issue 3, Pages 205-211
doi:10.1155/S0161171201003957
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
Abstract
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.