3 research outputs found
Some categorical aspects of BCH-algebras
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
On some classes of BCH-algebras
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