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

Abstract

This paper introduces the notions of atoms and atomicity in Calgebras and obtains a characterisation of atoms in the C-algebra of transformations. Further, this work presents some necessary conditions and sufficient conditions for the atomicity of C-algebras and shows that the class of finite atomic C-algebras is precisely that of finite adas. This paper also uses the if-then-else action to study the structure of C-algebras and classify the elements of the C-algebra of transformations.2010 Mathematics Subject Classification. 08A70, 03G25 and 68N15.