Boolean Algebra of C-Algebras

Guddati C. Rao (1Department of Mathematics, Andhra University, Visakhapatnam-530 003, India)
Perumali Sundarayya (2Department of Mathematics, GIT, GITAM University, Visakhapatnam-530 045, India)

Journal of Mathematical and Fundamental Sciences
Vol. 44 No. 3 (2012)

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 S(A) B of all C-algebras Sa, where a  B(A). It is also proved that B(A) is isomorphic to the Boolean algebra R(A) B of all C-algebras Aa, where a B(A).