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International Journal of Mathematics and Mathematical Sciences
Volume 2003 (2003), Issue 27, Pages 1739-1750
http://dx.doi.org/10.1155/S0161171203007634

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 Hindawi Publishing Corporation. 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.

Abstract

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.