<正> It is well known that the connected ring is one of the most useful rings. For example, in-tegral domain, local ring, PF ring and ring with torsion K0 group are all connected. LetX be a topological space. Then X is connected if and only if C(X) is a connected ring. Our main goal is to investigate the properties of connected rings by virtue of matrixtheories. Throughout this note, all rings are commutative with identity elements.