Boolean algebra of C-algebras

G.C. Rao¹ & P. Sundarayya^2
1Department of Mathematics, Andhra University, Visakhapatnam-530 003, India
²Department of Mathematics, GIT, GITAM University, Visakhapatnam-530 045, India
E-mails: gcraomaths@yahoo.co.in; psundarayya@yahoo.co.in

Abstract. A C- algebra is the algebraic form of the 3-valued conditional logic, which was introduced by F. Guzman and C. C. Squier in 1990. In this paper, some equivalent conditions for a C- algebra to become a boolean algebra in terms of congruences are given. It is proved that the set of all central elements B(A) is isomorphic to the Boolean algebra of all C-algebras Sa, where a B(A). It is also proved that B(A) is isomorphic to the Boolean algebra of all C-algebras Aa, where a B(A). 

Keywords: Boolean algebra; C-algebra; central element; permutable congruences.