This week's book giveaway is in the OCMJEA forum. We're giving away four copies of OCM Java EE 6 Enterprise Architect Exam Guide and have Paul Allen & Joseph Bambara on-line! See this thread for details.
There's no harm in class B declaring that it implements Serializable as well. It helps anyone looking at the source code or the javadocs, because they can see the implemented interfaces right away (without having to look at the superclass).