Not sure if I understand this question. Iβll try to answer anyway.
When you declare an abstract class Serializable, this interface is also inherited by subclasses, so they are considered Serializable and must also be serializable (if you do nothing, the default serialization mechanism will be applied to it, which may or may not work).
You only serialize instances of objects, not classes.
Serialization by default serializes the fields of the parent class, but only if this parent class is also Serializable. If not, the parent state is not serialized.
If you serialize an object of a subclass of an abstract class, and the abstract class is Serializable, then all the fields in this abstract parent class will also be serialized (the usual exceptions, such as transition or static fields apply).
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