Is boost::serialization::base_object required every time I do inheritance?

I have:

• non-polymorphic (no virtual methods) class hierarchy;

• base class already contains serialize;

• child classes are serialized directly;

    class A
    {
    private:
        int x;
        int y;
  
        template<typename Archive>
        void serialize(Archive& ar, const unsigned int)
        {
            ar & x & y;
        }
    };
  
    class B : public A { /* no data members*/ };
  
    class C : public A { /* no data members*/ };
  

1. Do I need serialize function in classes B and C? serialize function in B and C is exactly this:

    template<typename Archive>
    void serialize(Archive& ar, const unsigned int version)
    {
        ar & boost::serialization::base_object<A>(*this);
    }
   

2. Should I expect some notes in documentation about this?