International Journal of Mathematics and Mathematical Sciences
Volume 2012 (2012), Article ID 952654, 12 pages
Research Article

On BRK-Algebras

Department of Engineering Mathematics, GITAM University, Hyderabad Campus, Medak District, Andhra Pradesh 502 329, India

Received 31 December 2011; Revised 5 February 2012; Accepted 23 February 2012

Academic Editor: YoungBae Jun

Copyright © 2012 Ravi Kumar Bandaru. 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 notion of BRK-algebra is introduced which is a generalization of BCK/BCI/BCH/Q/QS/BM-algebras. The concepts of 𝐺 -part, 𝑝 -radical, medial of a BRK-algebra are introduced and studied their properties. We proved that the variety of all medial BRK-algebras is congruence permutable and showed that every associative BRK-algebra is a group.