Morphisms and Functor kerf in C-Algebras.

Let (A,B,f) be a C-algebra. For any subset N of B, its kernel kerfN is a subset of $\hat {\bf B}_f$. The kernel kerf has been used to obtain important results for C-algebras (see [2] and [4]). In this paper, we study further properties of kerf. In particular, for a transitional C-algebra (A,B,f) and quotient subsets M and N such that N ⊆ M and M is also a C-subset, we prove that $\widehat{({\bf M}/{\bf N})}_{\tilde f_{\bf N}|_{\langle {\bf M}/{\bf N}\rangle}} \cong_x \ker_f {\bf N}/ \ker_f {\bf M}$. In order to show this result, exact sequences in C-algebras are studied. Finally, we present a few examples and applications. [ABSTRACT FROM AUTHOR]