International Journal of Mathematics and Mathematical Sciences
Volume 2003 (2003), Issue 27, Pages 1739-1750
Some categorical aspects of BCH-algebras
1Department of Mathematical Sciences, College of Sciences, King Fahd University of Petroleum and Minerals, Dhahran 31261, Saudi Arabia
2Department of Mathematics, Islamia University, Bahawalpur, Pakistan
Received 14 May 2001
Copyright © 2003 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.
We show that the category BCH of BCH-algebras and
BCH-homomorphisms is complete. We also show that it has
coequalizers, kernel pairs, and an image factorization system. It
is also proved that onto homomorphisms and coequalizers, and
monomorphisms and one-to-one homomorphisms coincide,
respectively, in BCH. It is shown that MBCI is a coreflexive
subcategory of BCH. Regular homomorphisms have been defined and
their properties are studied. An open problem has been posed.