International Journal of Mathematics and Mathematical Sciences
Volume 29 (2002), Issue 7, Pages 417-425

On branchwise implicative BCI-algebras

Muhammad Anwar Chaudhry

Department of Mathematical Sciences, King Fahd University of Petroleum and Minerals, Dhahran 31261, Saudi Arabia

Received 19 April 2000

Copyright © 2002 Muhammad Anwar Chaudhry. 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 class of BCI-algebras, namely the class of branchwise implicative BCI-algebras. This class contains the class of implicative BCK-algebras, the class of weakly implicative BCI-algebras (Chaudhry, 1990), and the class of medial BCI-algebras. We investigate necessary and sufficient conditions for two types of BCI-algebras to be branchwise implicative BCI-algebras.