On the structure of C -algebras through atomicity and if-then-else

This paper investigates the notions of atoms and atomicity in C -algebras and obtains a characterisation of atoms in the C -algebra of transformations. In this connection, various characterisations for the existence of suprema of subsets of C -algebras are obtained. Further, this work presents some necessary conditions and some sufficient conditions for the atomicity of C -algebras and shows that the class of finite atomic C -algebras is precisely the class of finite adas. This paper also uses the intrinsic if-then-else action to study the structure of C -algebras and classify the elements of the C -algebra of transformations.